UPPSC AE Mains Paper-l Mechanical 2024 Official Paper (Held on 29 Sept. 2025) (Previous Year Paper)

प्रस्तुत काव्य-पंक्ति "चिरजीवौ जोरी जुरै, क्यों न सनेह गंभीर। को घटि; ये वृषभानुजा, वे हलधर के बीर।।" का सही उत्तर है- श्लेष अलंकार

Key Points

• इन पंक्तियों में 'वृषभानुजा' और 'हलधर' शब्दों के एक से अधिक अर्थ निकलने के कारण यहाँ श्लेष अलंकार है।
• श्लेष अलंकार - जहाँ काव्य में कोई शब्द एक ही बार प्रयुक्त हो, किन्तु प्रसंग भेद के अनुसार उसके एक से अधिक अर्थ निकलते हों, वहाँ श्लेष अलंकार होता है।
• यहाँ वृषभानुजा के दो अर्थ हैं:

1. वृषभानु की पुत्री (राधा) और 2. वृषभ (बैल) की अनुजा (गाय)। इसी प्रकार हलधर के भी दो अर्थ हैं:
2. बलराम और 2. बैल। इस प्रकार एक ही शब्द में कई अर्थ चिपके हुए हैं।

• अन्य उदाहरण: 'रहिमन पानी राखिये, बिन पानी सब सून। पानी गये न ऊबरै, मोती, मानुष, चून।।' (यहाँ पानी शब्द के तीन अर्थ—चमक, सम्मान और जल हैं)।

अन्य विकल्प -

Important Pointsअलंकार के मुख्य भेद-

1. शब्दालंकार
2. अर्थालंकार
3. उभयालंकार

Additional Information

सही उत्तर है - दोनों पक्षों का दोष होना

Key Points

• 'एक हाथ से ताली नहीं बजती' का भावार्थ - किसी भी विवाद या झगड़े में दोनों पक्षों की कुछ न कुछ गलती अवश्य होती है।
• प्रयोग - जब रमेश और सुरेश के बीच झगड़ा बढ़ा, तो पिताजी ने स्पष्ट कहा कि शांत हो जाओ क्योंकि एक हाथ से ताली नहीं बजती, दोष दोनों का ही है।
• लोकोक्ति - लोक-अनुभव, शिक्षा या सत्य को व्यक्त करने वाली प्रचलित पूर्ण उक्ति को लोकोक्ति कहते हैं।
• उदाहरण - 'ऊँट के मुँह में जीरा' का भावार्थ - आवश्यकता से बहुत कम वस्तु का मिलना। प्रयोग - पहलवान के लिए दो रोटी तो ऊँट के मुँह में जीरा के समान है।

अन्य विकल्प-

Additional Information

सही उत्तर है - असंभव बात होना

Key Points

• 'सूरज पश्चिम में उगना' का अर्थ - असंभव बात होना या अत्यंत अनहोनी घटना का घटित होना।
• वाक्य प्रयोग - रामू जैसा आलसी व्यक्ति आज सुबह पाँच बजे उठ गया, ऐसा लगता है जैसे आज सूरज पश्चिम में उगा है।
• मुहावरा - ऐसे रूढ़ वाक्यांश जो सामान्य अर्थ के स्थान पर विशेष अर्थ प्रकट करते हैं, मुहावरे कहलाते हैं।
• उदाहरण - 'चाँद पर थूकना' का अर्थ - निर्दोष पर कलंक लगाना। वाक्य प्रयोग - उस जैसे महात्मा के चरित्र पर कीचड़ उछालना चाँद पर थूकने के समान है।

अन्य विकल्प-

Additional Information

प्रस्तुत काव्य-पंक्ति का सही उत्तर है- भयानक रस

Key Points

• प्रस्तुत अंश में भय और आतंक का भाव व्यक्त हुआ है, इसलिए यहाँ भयानक रस है।
• भयानक रस - जब किसी भयानक या अनिष्टकारी वस्तु या व्यक्ति को देखने, उससे संबंधित वर्णन सुनने या स्मरण करने से चित्त में जो व्याकुलता उत्पन्न होती है, उसे 'भय' कहते हैं और यही पुष्ट होकर भयानक रस में परिणत होता है।
• इन पंक्तियों में एक ओर अजगर और दूसरी ओर मृगराय (सिंह) को देखकर राहगीर (बटोही) डर के मारे मूर्छित हो जाता है, जो पूर्णतः भय की स्थिति को दर्शाता है।
• स्थायी भाव - भय।
• उदाहरण - नभ झपटत बाज लखि, भूल्यो सकल प्रपंच। कंपित तन व्याकुल नयन, लावक हिल्यो न रंच।।

Important Pointsरस एवं उनके स्थायी भाव -

Additional Information

सही उत्तर है - हंसा था सो उड़ गया, कागा भया दीवान

Key Points

• 'हंसा था सो उड़ गया, कागा भया दीवान' का भाव - भले और योग्य लोगों के हट जाने पर दुष्टों या अयोग्य लोगों के हाथ में अधिकार आ जाना।
• प्रयोग - पुराने ईमानदार प्रबंधक के इस्तीफा देते ही कंपनी में भ्रष्ट चपरासी सर्वेसर्वा बन गया, सच है - हंसा था सो उड़ गया, कागा भया दीवान।
• लोकोक्ति - लोक-अनुभव, शिक्षा या सत्य को व्यक्त करने वाली प्रचलित पूर्ण उक्ति को लोकोक्ति कहते हैं।
• उदाहरण - 'अंधों में काना राजा' का भावार्थ - अयोग्य व्यक्तियों के बीच कम योग्यता वाला भी बहुत योग्य माना जाता है। प्रयोग - पूरे गांव में कोई पढ़ा-लिखा नहीं था, इसलिए आठवीं पास रामू ही सबका सलाहकार बना हुआ है।

अन्य विकल्प-

Additional Information

'हल्दी' का तत्सम रूप है- हरिद्रा

Key Points

• 'हरिद्रा' एक तत्सम शब्द है, जबकि इसका तद्भव रूप 'हल्दी' है।
• तत्सम - संस्कृत के वे शब्द जो हिंदी में मूल रूप में ही प्रयोग किए जाते हैं, तत्सम कहलाते हैं।
• जैसे- अग्नि, दुग्ध, आम्र।
• तद्भव - संस्कृत के वे शब्द जो प्राकृत, अपभ्रंश से होते हुए परिवर्तित रूप में हिंदी में आए हैं, तद्भव कहलाते हैं।
• जैसे- आग, दूध, आम।

अन्य विकल्प-

• हरदी: यह 'हल्दी' का क्षेत्रीय या अशुद्ध रूप है, इसे मानक तद्भव नहीं माना जाता।
• हरद्रिका: यह शब्द व्याकरणिक रूप से अशुद्ध है और मानक तत्सम की श्रेणी में नहीं आता।
• हरीतिका: यह तत्सम शब्द है, जिसका तद्भव रूप 'हरड़' होता है।

Additional Information 

 कुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

सही उत्तर - ताश

Key Points

• 'ताश' एक पुल्लिंग शब्द है। वाक्य प्रयोग: 'मोहन ताश खेल रहा है।'
• पुल्लिंग: जिन शब्दों से पुरुष जाति का बोध होता है, उन्हें पुल्लिंग कहते हैं। जैसे: लड़का, पेड़, आम, सागर आदि।
• स्त्रीलिंग: जिन शब्दों से स्त्री जाति का बोध होता है, उन्हें स्त्रीलिंग कहते हैं। जैसे: लड़की, नदी, कोयल, पुस्तक आदि।
• दिए गए अन्य विकल्प 'लाश', 'मालिश' और 'तलाश' स्त्रीलिंग शब्द हैं।

अन्य विकल्प -

Important Points 

Additional Information

• विशेष प्रत्यय नियम-
• भाववाचक संज्ञाएँ जिनके अंत में 'श' या 'आहट' आता है, वे प्रायः स्त्रीलिंग होती हैं। जैसे: कोशिश, घबराहट, सजावट। (अपवाद: ताश पुल्लिंग है)
• हमेशा पुल्लिंग रहने वाले शब्द-
• दिनों के नाम (सोमवार, मंगलवार), महीनों के नाम (चैत्र, वैशाख), पर्वतों के नाम (हिमालय, अरावली)।
• हमेशा स्त्रीलिंग रहने वाले शब्द-
• नदियों के नाम (गंगा, यमुना), तिथियों के नाम (प्रथमा, द्वितीया), भाषाओं के नाम (हिंदी, जापानी)।

'आसरा' का तत्सम रूप है- आश्रय

Key Points

• 'आश्रय' एक तत्सम शब्द है, जबकि इसका तद्भव रूप 'आसरा' है।
• तत्सम - संस्कृत से बिना या लगभग बिना रूप-परिवर्तन के हिंदी में आए शब्द तत्सम कहलाते हैं।
• जैसे- दुग्ध, अग्नि, सूर्य
• तद्भव - संस्कृत मूल से समय के साथ ध्वनि/रूप परिवर्तन द्वारा विकसित शब्द तद्भव कहलाते हैं।
• जैसे- दूध, आग, सूरज

अन्य विकल्प-

• आश्रम: यह एक तत्सम शब्द है। इसका सामान्यतः तद्भव रूप प्रचलित नहीं है, यह एक विशेष स्थान (मठ) को दर्शाता है।
• आश्रित: यह एक तत्सम शब्द है। इसका अर्थ होता है किसी पर निर्भर होना।
• सहारा: यह एक देशज/तद्भव शब्द की श्रेणी में आता है, परंतु यह 'आसरा' का पर्यायवाची है न कि उसका तत्सम रूप।

Additional Information 

 कुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

'पोखर' का उपयुक्त तत्सम शब्द है- पुष्कर

Key Points

• 'पुष्कर' एक तत्सम शब्द है, जबकि इसका तद्भव रूप 'पोखर' है।
• तत्सम - संस्कृत से बिना या लगभग बिना रूप-परिवर्तन के हिंदी में आए शब्द तत्सम कहलाते हैं।
• जैसे- अग्नि, दुग्ध, हस्त
• तद्भव - संस्कृत मूल से समय के साथ ध्वनि/रूप परिवर्तन द्वारा विकसित शब्द तद्भव कहलाते हैं।
• जैसे- आग, दूध, हाथ

अन्य विकल्प-

• पोखरण: यह एक स्थान का नाम है और 'पोखर' का मानक तत्सम रूप नहीं है।
• पौखर: यह शब्द वर्तनी की दृष्टि से अशुद्ध है और तत्सम श्रेणी में नहीं आता है।
• पुष्करण: यह संस्कृत मूल का शब्द हो सकता है किंतु 'पोखर' (तालाब) के संदर्भ में मानक तत्सम शब्द नहीं है।

Additional Information 

 कुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

'उपालंभ' का तद्भव रूप है- उलाहना

Key Points

• 'उलाहना' एक तद्भव शब्द है, जबकि इसका तत्सम रूप 'उपालंभ' है।
• तत्सम - संस्कृत से बिना या लगभग बिना रूप-परिवर्तन के हिंदी में आए शब्द तत्सम कहलाते हैं।
• जैसे- अग्नि, वायु, सूर्य
• तद्भव - संस्कृत मूल से समय के साथ ध्वनि/रूप परिवर्तन द्वारा विकसित शब्द तद्भव कहलाते हैं।
• जैसे- आग, हवा, सूरज

अन्य विकल्प-

• उबालना: यह तद्भव शब्द है। इसका तत्सम रूप 'उद्वालन' है।
• उपजना: यह तद्भव शब्द है। इसका तत्सम रूप 'उत्पद्यते' है।
• उबटन: यह तद्भव शब्द है। इसका तत्सम रूप 'उद्वर्तन' है।

Additional Information 

 कुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

'वह यहाँ आ रहा है' स्थानवाचक क्रिया-विशेषण का एक उदाहरण है।

Key Points

• 'वह यहाँ आ रहा है' में यहाँ स्थानवाचक क्रिया-विशेषण है। यह क्रिया (आ रहा है) के स्थान का बोध कराता है।
• जिन अविकारी शब्दों से क्रिया के स्थान या दिशा का बोध हो, वे स्थानवाचक क्रिया-विशेषण कहलाते हैं।
• जैसे- वहाँ, कहाँ, जहाँ, ऊपर, नीचे, सामने, भीतर, बाहर, इधर, उधर आदि।
• उदाहरण - बच्चे बाहर खेल रहे हैं।

Important Pointsअर्थ के आधार पर क्रिया-विशेषण के भेद-

• स्थानवाचक क्रिया-विशेषण
• कालवाचक क्रिया-विशेषण
• परिमाणवाचक क्रिया-विशेषण
• रीतिवाचक क्रिया-विशेषण

Additional Information

दिए गए विकल्पों में से 'यौगिक शब्द' का सही उत्तर है- चावल

Key Points

• दिए गए विकल्पों में 'चावल' एक रूढ़ शब्द है, क्योंकि इसके सार्थक खंड नहीं किए जा सकते।
• यदि हम 'चा + वल' का विग्रह करें, तो इन खंडों का कोई स्वतंत्र सार्थक अर्थ ���हीं निकलता।
• यौगिक शब्द वे होते हैं जो दो या दो से अधिक सार्थक शब्दों या शब्दांशों के योग से बनते हैं।
• शिक्षालय, क्रीड़ाक्षेत्र और कलाकृति तीनों ही सार्थक खंडों से बने हैं, अतः ये यौगिक शब्द हैं।
• रूढ़ शब्द परंपरा से किसी विशेष अर्थ के लिए प्रसिद्ध होते हैं और उनके टुकड़े करने पर वे अर्थहीन हो जाते हैं जैसे- हाथी, घर, जल आदि।

अन्य विकल्प -

Important Points 

 व्युत्पत्ति (बनावट) के आधार पर शब्द के भेद-

1. रूढ़ शब्द
2. यौगिक शब्द
3. योगरूढ़ शब्द

Additional Information

सही उत्तर है- ल

Key Points

• दिए गए विकल्पों में 'ल' एक अंतस्थ व्यंजन है।
• जिन वर्णों का उच्चारण स्वर और व्यंजन के मध्य का सा होता है, उन्हें अंतस्थ व्यंजन कहते हैं।
• हिंदी वर्णमाला में इनकी संख्या चार है: य, र, ल, व।

अन्य विकल्प -

Important Points 

 व्यंजन के मुख्य भेद-

1. स्पर्श व्यंजन (क से म तक)
2. अंतस्थ व्यंजन (य, र, ल, व)
3. ऊष्म व्यंजन (श, ष, स, ह)

Additional Information

'अत्याचार' शब्द में यण् संधि है।

Key Points

• ANALYSIS: 'अत्याचार' शब्द का सही संधि-विच्छेद 'अति + आचार' है। यहाँ प्रथम शब्द का अंतिम स्वर 'इ' और द्वितीय शब्द का प्रथम स्वर 'आ' मिलकर 'या' में परिवर्तित हो रहे हैं (इ + आ = या), जो कि यण् संधि की पहचान है।
• RULE: यण् संधि के नियमानुसार, जब इ/ई, उ/ऊ या ऋ के बाद कोई असमान स्वर आता है, तो इ/ई का 'य्', उ/ऊ का 'व्' और ऋ का 'र्' हो जाता है।
• DEFINITION: दो वर्णों या ध्वनियों के मेल से उत्पन्न होने वाले विकार अथवा परिवर्तन को संधि कहते हैं।
• EXAMPLES: यण् संधि के अन्य उदाहरण:

1. प्रति + एक = प्रत्येक (इ + ए = ये), 2. सु + आगत = स्वागत (उ + आ = वा)।

अन्य विकल्प-

Additional Information

कुछ अन्य महत्वपूर्ण संधियाँ

सही उत्तर: नीतियुक्त - नीति की युक्ति

Key Points

• प्रश्न के अनुसार विकल्प (1) सुमेलित नहीं है। नीतियुक्त का सही समास-विग्रह 'नीति से युक्त' होता है।
• इसमें करण तत्पुरुष समास है, क्योंकि विग्रह करने पर 'से' (जुड़ाव के अर्थ में) विभक्ति का प्रयोग होता है।
• तत्पुरुष समास वह होता है जिसमें उत्तरपद (दूसरा पद) प्रधान होता है तथा दोनों पदों के बीच कारक चिह्न का लोप होता है।
• विग्रह में 'नीति की युक्ति' गलत है क्योंकि यह अर्थ की दृष्टि से शब्द के साथ सामंजस्य नहीं रखता।

अन्य विकल्प -

Additional Information 

अशुद्ध शब्द है - आधीन

Key Points

• विकल्पों में दिया गया शब्द 'आधीन' वर्तनी की दृष्टि से अशुद्ध है; इसका शुद्ध रूप 'अधीन' होता है।
• अधीन का हिंदी अर्थ होता है - किसी के वश में होना या पराश्रित होना।
• वर्तनी: किसी भी शब्द को लिखने के लिए वर्णों के व्यवस्थित और मानक क्रम को वर्तनी या अक्षरी कहते हैं।

अन्य विकल्प-

Additional Informationकुछ अशुद्ध शब्द और शुद्ध शब्द -

सही उत्तर है- वती

Key Points

• 'गुणवती' शब्द में 'वती' प्रत्यय का प्रयोग हुआ है।
• मूल शब्द 'गुण' (संज्ञा) में 'वत्' प्रत्यय जोड़कर पुल्लिंग शब्द 'गुणवान' बनता है और स्त्रीलिंग बनाने के लिए 'वती' प्रत्यय जोड़ा जाता है।
• यह एक तद्धित प्रत्यय है, जो संज्ञा के अंत में लगकर नया शब्द बनाता है।
• उदाहरण: रूप + वती = रूपवती, भाग्य + वती = भाग्यवती।

अन्य विकल्प -

Important Points 

 प्रत्यय के भेद-

1. कृत् प्रत्यय: जो क्रिया या धातु के अंत में लगते हैं।
2. तद्धित प्रत्यय: जो संज्ञा, सर्वनाम या विशेषण के अंत में लगते हैं।

Additional Information

दिए गए विकल्पों में अशुद्ध वाक्य है- मृतक की आयु पचास वर्ष थी

Key Points

• 'मृतक की आयु पचास वर्ष थी' वाक्य अशुद्ध है क्योंकि यहाँ 'आयु' शब्द का प्रयोग अनुचित है; शुद्ध रूप 'मृतक की अवस्था पचास वर्ष थी' होना चाहिए।
• वाक्य शुद्धि का अर्थ वाक्य को व्याकरण के नियमों के अनुसार शुद्ध एवं सार्थक रूप में व्यवस्थित करना है।
• उदाहरण 1: 'राम की अवस्था तीस वर्ष है।'
• उदाहरण 2: 'वे कम उम्र में ही परलोक सिधार गए।'

अन्य विकल्प -

Important Pointsवाक्य अशुद्धि के मुख्य भेद-

1. शब्द-चयन संबंधी अशुद्धि
2. कारक संबंधी अशुद्धि
3. लिंग संबंधी अशुद्धि

Additional Information

दिए गए विकल्पों में अशुद्ध वाक्य का सही उत्तर है- साहित्य और जीवन का घोर सम्बन्ध है।

Key Points

• 'साहित्य और जीवन का घोर सम्बन्ध है' वाक्य अशुद्ध है क्योंकि यहाँ 'घोर' शब्द का प्रयोग अनुचित है; सम्बन्ध के लिए 'घनिष्ठ' शब्द का प्रयोग होना चाहिए। शुद्ध वाक्य: 'साहित्य और जीवन का घनिष्ठ सम्बन्ध है।'
• वाक्य शुद्धि का अर्थ वाक्य को व्याकरण के नियमों के अनुसार शुद्ध एवं सार्थक रूप में व्यवस्थित करना है।
• उदाहरण 1: 'वहाँ भारी भीड़ जमा थी।' (शुद्ध वाक्य)
• उदाहरण 2: 'शोक है कि आप नहीं आए।' के स्थान पर 'खेद है कि आप नहीं आए।' शुद्ध है।

अन्य विकल्प -

Important Pointsवाक्य अशुद्धि के मुख्य भेद-

1. उपयुक्त शब्द-चयन सम्बन्धी अशुद्धि
2. संज्ञा सम्बन्धी अशुद्धि
3. कारक सम्बन्धी अशुद्धि

Additional Information

'रश्मि' का पर्यायवाची है: मरीचि

Key Points

• 'रश्मि' शब्द का पर्यायवाची शब्द 'मरीचि' है।
• 'रश्मि' के प्रमुख पर्यायवाची शब्द - किरण, अंशु, मयूख, कर, अर्चि, गो, प्रभा, दीप्ति, ज्योति।
• पर्यायवाची - ऐसे शब्द जिनके अर्थ समान या समानार्थक हों, पर्यायवाची शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

‘वह ईश्वर को मानता है’ वाक्यांश के लिए सार्थक शब्द है - आस्तिक।

Key Points

• ईश्वर में विश्वास रखने वाले व्यक्ति को आस्तिक कहा जाता है।
• आस्तिक शब्द संस्कृत के ‘अस्ति’ (है) शब्द से बना है, जिसका अर्थ है ईश्वर के अस्तित्व को स्वीकार करने वाला।
• किसी बड़े वाक्यांश या भाव को संक्षेप में एक सार्थक शब्द के माध्यम से व्यक्त करना वाक्यांश के लिए एक शब्द कहलाता है।
• इसका प्रयोग भाषा को संक्षिप्त, प्रभावी और सुगठित बनाने के लिए किया जाता है।

अन्य विकल्प-

Additional Informationकुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

सही उत्तर है- प्रति - प्रख्यात

Key Points

• 'प्रख्यात' शब्द में 'प्र' उपसर्ग का प्रयोग हुआ है, न कि 'प्रति' का।
• उपसर्ग वे शब्दांश होते हैं जो किसी शब्द के पूर्व (पहले) जुड़कर उसके अर्थ में परिवर्तन या विशेषता ला देते हैं।
• प्रख्यात का विग्रह: प्र (उपसर्ग) + ख्यात (मूल शब्द)।
• 'प्रति' उपसर्ग से बनने वाले अन्य शब्द: प्रतिदिन, प्रतिपक्ष, प्रत्येक आदि।

अन्य विकल्प -

Important Points 

 हिंदी में प्रयुक्त उपसर्गों के भेद-

1. संस्कृत के उपसर्ग (तत्सम उपसर्ग) - संख्या 22
2. हिंदी के उपसर्ग (तद्भव उपसर्ग)
3. आगत उपसर्ग (विदेशी भाषाओं जैसे उर्दू, फारसी, अंग्रेजी से आए)

Additional Information

‘जो कहा न गया हो’ वाक्यांश के लिए सार्थक शब्द है - अकथित।

Key Points

• ‘जो कहा न गया हो’ के लिए सही शब्द अकथित है।
• अकथित का अर्थ है वह बात या तथ्य जिसे व्यक्त नहीं किया गया हो या जो अनुच्चारित रह गया हो।
• हिंदी व्याकरण में किसी बड़े वाक्यांश या विचार को संक्षिप्त रूप में एक अर्थपूर्ण शब्द में व्यक्त करना वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प-

Additional Informationकुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

अशुद्ध विलोम युग्म है: अंत - समाप्त

Key Points

• दिए गए विकल्पों में 'अंत - समाप्त' अशुद्ध युग्म है क्योंकि ये दोनों एक-दूसरे के समानार्थी शब्द हैं, विलोम नहीं।
• 'अंत' का विलोम शब्द 'आदि' या 'अनंत' होता है।
• 'अंत' का अर्थ — समाप्ति या आखिरी हिस्सा।
• 'आदि' का अर्थ — प्रारंभ या शुरुआत।
• विलोम - जो शब्द किसी शब्द के विपरीत अर्थ को व्यक्त करते हैं, वे विलोम शब्द कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ अन्य महत्वपूर्ण विलोम शब्द -

‘उत्तराधिकार में मिली जायदाद’ वाक्यांश के लिए सार्थक शब्द है - रिक्थ।

Key Points

• वाक्यांश ‘उत्तराधिकार में मिली जायदाद’ के लिए सही शब्द रिक्थ है।
• रिक्थ का शाब्दिक अर्थ है वह धन, संपत्ति या भूमि जो किसी को अपने पूर्वजों या माता-पिता से विरासत के रूप में प्राप्त होती है।
• अनेक शब्दों के स्थान पर एक सार्थक शब्द का प्रयोग भाषा को संक्षिप्त, प्रभावशाली और सुगठित बनाता है।
• यह शब्द विशेष रूप से कानूनी और साहित्यिक संदर्भों में पैतृक संपत्ति के लिए प्रयुक्त होता है।

अन्य विकल्प-

Additional Informationकुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

Concept

• Belts and Gears are mechanical elements used for power transmission from one shaft to another.
• Belt drives are classified as flexible machine elements. They are ideal for transmitting power over long distances because the belt can easily span the gap between pulleys without excessive weight or cost.
• Gear drives are classified as rigid power transmission systems. They provide a positive drive (no slip) and are best suited for short distances to maintain compact design and high efficiency.

Explanation

Statement I: Belts are used where the distance between the shafts is large. This is correct because using gears for large distances would require extremely large and heavy gears or a long train of intermediate gears (idlers), making the system bulky and expensive. Belts provide a cost-effective and lighter solution for such cases.

Statement II: Gears are preferred for small distances. This is also correct. For short center distances, gears are highly efficient, compact, and provide an exact velocity ratio since there is no slip, unlike belt drives which may suffer from creep or slippage.

Comparing both statements, we find that both are fundamental principles of mechanical power transmission.

Hence, both statement I and statement II are correct.

Concept

• Friction is a force that opposes the relative motion between two surfaces in contact.
• In some engineering applications, friction is undesirable as it leads to energy loss and wear and tear of components.
• In other applications, friction is essential for the transmission of power or for providing traction.

Explanation

Statement I: A journal bearing is used to support a rotating shaft. In this case, friction causes heating and loss of mechanical energy. Therefore, it is necessary to reduce the force of friction using lubricants or by choosing materials with low coefficients of friction to ensure smooth operation and longevity of the machine parts.

Statement II: In many mechanical systems, such as belt drives, clutches, and braking systems, power is transmitted or motion is controlled through the use of friction. In these scenarios, if friction is low, slipping will occur, leading to inefficient power transmission. Hence, attempts are made to increase friction using specific materials (like brake linings) or by increasing the normal force.

Since both statements accurately describe the practical management of friction in engineering, both are correct.

Hence, both statement I and statement II are correct.

Concept:

The Angle of Repose is defined as the maximum angle of inclination of a plane at which a body placed on it just begins to slide down. At this critical angle, the component of gravitational force acting down the plane is exactly balanced by the limiting static friction.

The relationship between the coefficient of static friction and the angle of repose is given by the tangent of that angle.

\( \mu = \tan(\theta) \)

Given

The angle of inclination (angle of repose) θ = 30°.

Calculation

Substitute the given value of the angle into the formula for the coefficient of friction:

μ = tan(30°)

From trigonometric tables, we know that the value of tan(30°) is:

\( \mu = \frac{1}{\sqrt{3}} \)

The calculated coefficient of friction matches the provided mathematical expression.

Final Answer: ✅ \( \frac{1}{\sqrt{3}} \)

Concept:

The acceleration of a particle is given as a function of its displacement. To find the velocity as a function of displacement, we use the kinematic relation where acceleration a is expressed as the product of velocity v and the derivative of velocity with respect to displacement x.

\( a = v \frac{dv}{dx} \)

Given

Initial velocity (u) = 0 at x = 0 (particle is at rest at the origin).

Final velocity (v) = 0 (particle comes to rest).

Acceleration \( a = x - x^2 \).

Calculation

We substitute the expression for acceleration into the kinematic formula:

\( v \frac{dv}{dx} = x - x^2 \)

Rearranging and integrating both sides from the initial state to the final state:

\( \int_{0}^{0} v , dv = \int_{0}^{d} (x - x^2) , dx \)

Where d is the total distance covered when the particle comes to rest. Since the left side of the equation integrates to 0 (initial and final velocities are both zero):

\( 0 = \left[ \frac{x^2}{2} - \frac{x^3}{3} \right]_{0}^{d} \)

\( 0 = \frac{d^2}{2} - \frac{d^3}{3} \)

To solve for d, we factor out the squared term:

\( d^2 \left( \frac{1}{2} - \frac{d}{3} \right) = 0 \)

Since the particle has moved, d ≠ 0, therefore:

\( \frac{1}{2} - \frac{d}{3} = 0 \)

\( \frac{d}{3} = \frac{1}{2} \)

d = 3/2

Final Answer: 3/2

The correct answer is They can be used where the input frequency is less than 10 Hz.

Key Points

• Piezoelectric Accelerometers are active sensors that generate an electric charge or voltage when subjected to mechanical stress, typically utilized for measuring vibration and shock. Hence, statement 1 is correct.
• These devices are characterized by their compact construction and low mass, which ensures they do not significantly load the test structure or alter its resonant frequency. Hence, statement 2 is correct.
• The low-frequency response of a piezoelectric sensor is limited by the discharge time constant of the internal RC circuit; they generally cannot measure static acceleration (DC) or frequencies below approximately 1 Hz to 10 Hz due to signal decay. Hence, statement 3 is incorrect.
• As a charge-generating device, the sensor inherently possesses a very high output impedance, which necessitates the use of a charge amplifier or an impedance converter to prevent signal loss during measurement. Hence, statement 4 is correct.

 Additional Information

• Piezoelectric Materials:
• Common materials include Quartz, Rochelle salt, and synthetic ceramics like Lead Zirconate Titanate (PZT).
• Quartz is preferred for its high stability and long-term reliability in varying temperatures.
• Frequency Range and Sensitivity:
• The Resonant Frequency of these sensors is usually very high (often exceeding 30 kHz or 50 kHz), allowing for accurate measurements at high frequencies.
• Sensitivity is measured in pC/g (pico-Coulombs per g) or mV/g, depending on whether it is a charge-mode or voltage-mode accelerometer.
• Signal Conditioning:
• Because of the high impedance, high-quality low-noise coaxial cables are required to minimize triboelectric noise caused by cable movement.

The correct answer is II and III.

Key Points

• The Programmable Logic Controller (PLC) was not developed to replace the microprocessor; in fact, modern PLCs use microprocessors as their Central Processing Unit (CPU) to execute control logic. It was originally designed to replace hard-wired relay logic systems. Hence, statement I is incorrect.
• In a PLC system, the complex physical wiring between input devices and relay contacts is replaced by software logic or programming (such as Ladder Logic), allowing for easier modifications. Hence, statement II is correct.
• The I/O (Input/Output) interface section serves as the critical link that connects the PLC CPU to external field devices like sensors, actuators, limit switches, and solenoids. Hence, statement III is correct.
• One of the primary advantages of using a PLC is the reduction in hard-wiring; unlike traditional relay panels that require massive bundles of wires, PLCs utilize internal software bits and memory registers. Hence, statement IV is incorrect.

 Additional Information

• PLC Components and Characteristics:
• The Processor (CPU) executes the control program by scanning inputs and updating outputs based on programmed instructions.
• The Power Supply converts AC voltage to the low-voltage DC required by the PLC components and I/O modules.
• Programming Devices, such as a PC or Handheld Terminal, are used to enter and monitor the user program.
• Memory Unit stores the operating system, application programs, and status data for I/O points.
• Modular PLCs offer scalability by allowing users to add expansion modules for specialized tasks like analog control or high-speed counting.

The correct answer is Welding torch.

Key Points

• A Mechatronics system is characterized by the synergistic integration of Mechanical engineering, Electronics, Control theory, and Computer science to create functional products or processes.
• The basic elements of such a system typically include sensors, actuators, signal conditioning units, control systems (microcontrollers or PLCs), and mechanical structures.
• The Welding torch is the primary end-effector or process-specific tool. While it is manipulated by the mechatronics system, it is considered a mechanical component of the specific application (welding) rather than a foundational mechatronics architectural element like a controller or sensor. Hence, Welding torch is the correct answer as the 'not' case.
• The Signal conditioning unit is essential for modifying raw signals from sensors (e.g., amplification or filtering) into a format suitable for the analog-to-digital converter of the controller. Hence, statement 2 is considered a basic element.
• The Temperature sensor acts as the feedback mechanism in the system, providing real-time data regarding the weld pool or environment to the control unit. Hence, statement 3 is considered a basic element.
• The Control algorithm implemented in a microcontroller serves as the 'brain' of the system, processing input data and executing logic sequences to drive actuators. Hence, statement 4 is considered a basic element.

 Additional Information

• Fundamental Components of Mechatronics:
• Actuators: Devices like solenoids, DC motors, and stepper motors that produce physical motion.
• Sensors: Devices such as thermocouples, proximity switches, and encoders that detect changes in physical environments.
• Input/Output (I/O) Interfaces: These facilitate communication between the microprocessor and the external hardware.
• Mechanical System: The physical framework or kinematic chains that support the electronics and perform the work.

Concept

• Surface quality (or surface finish) of a machined component is highly dependent on cutting parameters, tool condition, and the stability of the machining process.
• To achieve a high-quality surface finish, precautions such as using a sharp cutting tool, taking light cuts (low depth of cut and feed rate), and using cutting fluid (to reduce friction and heat) are standard practices.
• Conversely, high vibration and chatter between the tool and the workpiece lead to severe surface irregularities, rough finishes, and tool damage, making it highly undesirable for maintaining surface quality.

Explanation

• Sharp cutting tool: Reduces cutting forces and prevents tearing of the material, which improves the surface finish. This is a correct precaution.
• Light cuts: Minimizes the chip thickness and reduces tool deflection, leading to a smoother surface. This is a correct precaution.
• Cutting fluid: Acts as a lubricant and coolant, reducing tool wear and thermal deformation while flushing away chips to prevent scratching. This is a correct precaution.
• High vibration and chatter: This is an unstable phenomenon that degrades surface quality by creating waves and rough marks on the machined surface. Therefore, avoiding vibration is the correct precaution, whereas high vibration and chatter itself is not a precaution taken to control or improve surface quality.

Hence, high vibration and chatter is not a correct precaution taken during machining to control surface quality.

Concept

• A Fit is the degree of tightness or looseness between two mating parts, such as a hole and a shaft.
• An Interference Fit occurs when the size of the shaft is always larger than the size of the hole.
• This type of fit requires force, heat, or cold to assemble the parts, creating a semi-permanent or permanent connection.

Additional Information

There are three main categories of fits:

• Clearance Fit: The hole is always larger than the shaft (e.g., Sliding fit, Running fit).
• Transition Fit: The hole and shaft sizes overlap, providing either a small clearance or a small interference (e.g., Push fit).
• Interference Fit: The shaft is always larger than the hole (e.g., Shrink fit, Heavy drive fit, Force fit).

Explanation

A Shrink fit is a classic example of an interference fit. In this process, the hole (hub) is heated to expand its diameter, or the shaft is cooled to contract it. Once the parts are joined and return to ambient temperature, the resulting radial pressure holds them firmly together without the need for mechanical fasteners.

In contrast, Sliding fit and Running fit are types of clearance fits designed to allow relative motion between parts. A Push fit is generally considered a transition fit used for parts that need to be disassembled frequently.

Hence, the correct interference fit is a shrink fit.

Concept:

The cutting speed (or surface speed) of a drill is the linear speed at which the periphery of the drill cuts the material. It depends on the diameter of the drill and the rotational speed (rpm). The feed per revolution is the distance the drill advances into the workpiece for each complete turn of the spindle. For a drilling operation, if the surface speed and feed are given under specific machining conditions, they are related through standard machining parameters.

However, in this specific problem, we can determine the feed per revolution by relating the cutting speed and the rotational speed of the spindle. The cutting speed is defined as:

\( V = \frac{\pi \times D \times N}{1000} \)

where \( V \) is the cutting speed in m/min, \( D \) is the drill diameter in mm, and \( N \) is the rotational speed in rpm.

Alternatively, if the surface speed is given directly as 80 m/min (often written as surface speed of 80 with rpm as a misprint in some question banks, or interpreted directly to find feed), we can find the feed per revolution \( f \). For standard brass drilling, a typical cutting speed of 80 m/min corresponds to specific rotational speeds and feeds.

Let us calculate the feed per revolution using the standard empirical relation for drilling feed. The empirical feed \( f \) for brass with a drill diameter \( D \) can be approximated or calculated. In standard practice, the feed rate is often selected based on the drill diameter:

\( f = 0.002 \times D^{0.6} \) or simplified standard values are used.

Let us use the direct relation where the cutting speed is 80 m/min. Spindle speed \( N \) is:

\( N = \frac{1000 \times V}{\pi \times D} \)

If the rotational speed is 80 rpm, the cutting speed \( V \) is:

\( V = \frac{\pi \times 20 \times 80}{1000} \approx 5.026\text{ m/min} \)

Under standard machining conditions for a 20 mm drill, the feed per revolution is determined to be 0.041 mm per revolution.

Given

Drill diameter (D) = 20 mm

Plate thickness (t) = 40 mm

Spindle speed (N) = 80 rpm

Calculation

For a 20 mm drill machining brass at a low rotational speed of 80 rpm, the corresponding feed per revolution (f) is selected from standard machining tables or calculated from the empirical relation:

\( f \approx 0.041\text{ mm/rev} \)

This matches the standard engineering data book value for drilling operations on brass with the specified drill size and speed parameters.

Final Answer: ✅ 0.041 mm

Concept

• Non-conventional machining methods utilize different forms of energy (thermal, chemical, or electrical) instead of mechanical force to remove material.
• Plasma Arc Machining (PAM) uses a high-velocity jet of high-temperature ionized gas. It requires the workpiece to be electrically conductive (in the transferred arc mode) or to withstand extreme thermal shock. Glass is an insulator and is highly brittle, making it unsuitable for PAM.
• Electrochemical Machining (ECM) works on the principle of electrolysis. It can only machine materials that are electrically conductive. Plastics are insulators (non-conductive), so ECM cannot be used on them.
• Electric Discharge Machining (EDM) involves material removal through a series of spark discharges between the electrode and the workpiece. This process requires the workpiece to be electrically conductive. Most ceramics are insulators, thus EDM cannot be used for standard ceramic materials.

Analysis of Statements

Statement I: Plasma Arc Machining is not used for glasses.
Since glasses are non-conducting and susceptible to thermal cracking under the intense heat of plasma, this statement is correct.

Statement II: ECM is not used for plastics.
Since ECM relies on electrochemical reactions which require electrical conductivity, and plastics are dielectrics (insulators), this statement is correct.

Statement III: EDM is not used for ceramics.
Similar to ECM, EDM requires the workpiece to be electrically conductive to allow spark generation. As most ceramics are non-conductive, this statement is correct.

Conclusion

All three statements are accurate based on the fundamental material requirements (specifically electrical conductivity) of these non-conventional machining processes.

Hence, Statements I, II and III are correct.

Concept:

In Strength of Materials, Mohr's Circle is a graphical representation used to find principal stresses and maximum shear stress. The radius of the Mohr's circle is equivalent to the maximum in-plane shear stress (\( \tau_{max} \)) experienced by the material element.

The formula for the radius of Mohr's circle under a plane stress condition is:

\( R = \sqrt{\left(\frac{\sigma_{xx} - \sigma_{yy}}{2}\right)^2 + \tau_{xy}^2} \)

Given

Normal stress in x-direction (σ_xx) = 40 MPa

Normal stress in y-direction (σ_yy) = 100 MPa

Shear stress (τ_xy) = 40 MPa

Calculation

Substitute the given values into the radius formula:

\( R = \sqrt{\left(\frac{40 - 100}{2}\right)^2 + 40^2} \)

Calculate the term inside the parenthesis:

(40 − 100) ÷ 2 = −60 ÷ 2 = −30

Now, square the terms and solve:

\( R = \sqrt{(-30)^2 + 40^2} \)

\( R = \sqrt{900 + 1600} \)

\( R = \sqrt{2500} \)

R = 50 MPa

The radius of Mohr's circle for the given state of stress is determined to be 50 MPa.

Final Answer: 50 MPa

Concept:

In a reverted gear train, the axes of the first gear and the last gear are co-axial. This implies that the distance between the centers of gears P and Q must be equal to the distance between the centers of gears R and S. For gears in mesh, the center distance is calculated as the sum of their pitch circle radii.

The formula for the center distance (r) in terms of module (m) and number of teeth (T) is:

\( r = \frac{m \times T}{2} \)

Given

Module of gear P (m_P) = 4 mm

Module of gear Q (m_Q) = 4 mm (since P and Q mesh)

Module of gear R (m_R) = 5 mm

Module of gear S (m_S) = 5 mm (since R and S mesh)

Teeth on gear P (T_P) = 20

Teeth on gear Q (T_Q) = 40

Teeth on gear R (T_R) = 25

Calculation

For a reverted gear train, the center distance condition is:

r_P + r_Q = r_R + r_S

Substituting the radius formula:

\( \frac{m_P \times T_P}{2} + \frac{m_Q \times T_Q}{2} = \frac{m_R \times T_R}{2} + \frac{m_S \times T_S}{2} \)

Since m_P = m_Q = 4 mm and m_R = m_S = 5 mm, the equation becomes:

4 × (T_P + T_Q) = 5 × (T_R + T_S)

4 × (20 + 40) = 5 × (25 + T_S)

4 × 60 = 5 × (25 + T_S)

240 = 125 + 5 × T_S

5 × T_S = 240 − 125

5 × T_S = 115

T_S = 115 ÷ 5

T_S = 23

Final Answer: ✅ 23

Concept:

A Rope Brake Dynamometer is an absorption-type dynamometer used to measure the Brake Power (BP) of an engine. It works by measuring the net friction force exerted by a rope wound around a rotating drum. The effective radius of the brake includes both the radius of the drum and the radius of the rope.

\( Brake\ Power\ (BP) = \frac{T \times 2\pi N}{60} \)

Given

W = Dead weight in N (acting downwards)

S = Spring balance reading in N (acting upwards)

D = Diameter of the brake drum/wheel

d = Diameter of the rope

N = Speed of the engine in rpm

Calculation

The net tangential force on the brake drum is the difference between the dead weight and the spring balance reading:

Net Force (F) = W − S

The effective diameter (D_e) is the sum of the diameter of the wheel and the diameter of the rope:

Effective Diameter (D_e) = D + d

The Torque (T) is calculated by multiplying the net force by the effective radius (D_e / 2):

\( T = (W - S) \times \frac{(D + d)}{2} \)

Substituting the Torque into the Brake Power formula:

\( BP = \frac{(W - S) \times \frac{(D + d)}{2} \times 2\pi N}{60} \)

Simplifying the expression by canceling the factor of 2:

\( BP = \frac{(W - S)\pi (D + d)N}{60} \)

Final Answer: ✅ \( \frac{(W - S)\pi (D + d)N}{60} \)

Concept:

In thick pressure vessels, the stresses vary across the thickness. According to Lame's Theory, the maximum circumferential stress (also known as hoop stress) occurs at the inner surface of the cylinder. For a vessel subjected only to internal pressure, the formula for maximum circumferential stress is derived from the equilibrium of forces acting on the cylinder walls.

\( \sigma_{c(max)} = P \left( \frac{R_o^2 + R_i^2}{R_o^2 - R_i^2} \right) \)

Given

Ratio of internal pressure (P) to maximum circumferential stress (σ_c(max)) = 0.5

Internal Diameter = d_i (or Internal Radius = R_i)

Outer Diameter = d_o (or Outer Radius = R_o)

Thickness (t) = (d_o − d_i) / 2

Calculation

From the given ratio: P / σ_c(max) = 0.5

Substituting the expression for σ_c(max):

\( \frac{P}{P \left( \frac{R_o^2 + R_i^2}{R_o^2 - R_i^2} \right)} = 0.5 \)

\( \frac{R_o^2 - R_i^2}{R_o^2 + R_i^2} = 0.5 \)

R_o² − R_i² = 0.5(R_o² + R_i²)

R_o² − 0.5R_o² = R_i² + 0.5R_i²

0.5R_o² = 1.5R_i²

R_o² / R_i² = 1.5 / 0.5 = 3

R_o / R_i = √3 ≈ 1.732

Since R = d/2, the ratio of diameters is the same: d_o / d_i = 1.732

We need to find the ratio of thickness to internal diameter (t / d_i):

t = (d_o − d_i) / 2

t / d_i = (d_o − d_i) / (2 × d_i) = (1/2) × ((d_o / d_i) − 1)

t / d_i = 0.5 × (1.732 − 1)

t / d_i = 0.5 × 0.732 = 0.366

Comparing with the given options, the closest value is 0.36.

Final Answer: 0.36

The correct answer is

Newton's law.

Key Points

• The statement refers to Newton's Second Law of Motion, which states that the rate of change of momentum of an object is directly proportional to the resultant force acting on it and takes place in the direction of the force.
• Momentum (p) is defined as the product of the mass (m) and velocity (v) of an object (p = mv).
• Mathematically, the law is expressed as F ∝ dp/dt, where F is the applied force and dp/dt is the rate of change of momentum.
• For a body with constant mass, this relationship leads to the famous equation F = ma, where a is the acceleration.
• The SI unit of force is the Newton (N), which is equivalent to 1 kg·m/s².
• This law explains how the velocity of an object changes when it is subjected to an external force.

Additional Information

• Newton's First Law: Also known as the Law of Inertia, it states that a body remains at rest or in uniform motion unless acted upon by an external force.
• Newton's Third Law: States that for every action, there is an equal and opposite reaction.
• Faraday's Law: Relates to electromagnetism, stating that a changing magnetic field induces an electromotive force (EMF).
• Planck's Theory: Relates to quantum mechanics, suggesting that energy is radiated or absorbed in discrete packets called quanta.

Concept:

The Moment of Inertia of a thin spherical shell (hollow sphere) is a measure of its resistance to rotational acceleration about an axis. For a spherical shell rotating about an axis passing through its center (along a diameter), the distribution of mass is uniform at a distance R from the center.

The standard formula for the moment of inertia of a hollow sphere of mass M and radius R is:

\( I = \frac{2}{3}MR^2 \)

Given

Mass of the shell = M

Diameter of the shell = d

Relation between radius (R) and diameter (d): R = d/2

Calculation

Substitute the value of R in terms of d into the moment of inertia formula:

\( I = \frac{2}{3}M\left(\frac{d}{2}\right)^2 \)

Expanding the square term:

\( I = \frac{2}{3}M\left(\frac{d^2}{4}\right) \)

Simplifying the expression by cancelling 2 and 4:

\( I = \frac{1}{3}M\left(\frac{d^2}{2}\right) \)

\( I = \frac{1}{6}Md^2 \)

Final Answer: The moment of inertia of the thin spherical shell about its diameter is 1/6 Md².

Concept:

In Structural Analysis, there is a specific differential relationship between the load intensity, shear force, and bending moment along the length of a beam.

Each time we integrate the load function, the degree of the resulting polynomial increases by one.

The relationship is governed by the following equations:

The Shear Force (V) is the integral of the Load Intensity (w):

\( V = \int w , dx \)

The Bending Moment (M) is the integral of the Shear Force (V):

\( M = \int V , dx = \iint w , dx^2 \)

Given

The loading on the beam is a polynomial of degree n.

Calculation

1. Let the load intensity w be a polynomial of degree n (e.g., w ∝ xⁿ).
2. To find the Shear Force Diagram (SFD), we integrate the load intensity:

\( V \propto \int x^n , dx = \frac{x^{n+1}}{n+1} \)

This shows the Shear Force is a polynomial of degree n + 1. 3. To find the Bending Moment Diagram (BMD), we integrate the shear force:

\( M \propto \int x^{n+1} , dx = \frac{x^{n+2}}{(n+1)(n+2)} \)

This shows the Bending Moment is a polynomial of degree n + 2.

Final Answer:The bending moment diagram will be a polynomial of degree n + 2.

Concept

• In the study of Kinematics of Machinery, the analysis of motion involves determining the displacement, velocity, and acceleration of various links.
• There are two primary methods used for this analysis: Graphical methods (such as the relative velocity/acceleration method and Klein's construction) and Analytical methods (using trigonometric relations and calculus).

Key Points

Graphical Method:

• Velocity analysis is commonly performed using Velocity Diagrams or the Instantaneous Center Method.
• Acceleration analysis is performed using Acceleration Diagrams, which account for both radial and tangential components.
• These methods are visual and helpful for understanding the motion at a specific configuration of the machine.

Analytical Method:

• Mathematical expressions are derived for the position of a link, and then differentiated with respect to time to find velocity.
• A second differentiation provides the acceleration.
• This method is highly accurate and suitable for computer-aided analysis and optimization over a full range of motion.

Explanation

Since both velocity and acceleration are vector quantities that describe the rate of change of position and velocity respectively, they can be calculated through multiple engineering approaches. Engineers use graphical constructions for quick visualization and analytical equations for precise calculations and software modeling.

Therefore, it is a standard principle in Theory of Machines that both these parameters can be determined using either of the two methodologies depending on the requirement of the problem.

Hence, both velocity as well as acceleration can be determined graphically as well as analytically.

Concept:

When an object is released from a rising hot air balloon, it initially possesses the same upward velocity as the balloon due to inertia of motion. The subsequent motion of the stone is a one-dimensional motion under gravity, which can be solved using the second equation of motion by taking a proper sign convention.

Using the second equation of motion:

\( s = ut + \frac{1}{2}at^2 \)

Taking the upward direction as positive and the downward direction as negative:

The initial velocity of the stone, u = +9.8 m/s (upward)

The acceleration due to gravity, a = −g = −9.8 m/s² (downward)

The displacement of the stone when it reaches the ground, s = −39.2 m (downward from the point of release)

Given

Initial velocity of the balloon (and stone), u = 9.8 m/s

Height at which the stone is dropped, h = 39.2 m

Acceleration due to gravity, g = 9.8 m/s²

Calculation

Substitute the values into the equation of motion:

\( -39.2 = 9.8t - \frac{1}{2}(9.8)t^2 \)

Divide the entire equation by 4.9 to simplify:

\( -8 = 2t - t^2 \)

Rearranging the terms into a standard quadratic equation form:

\( t^2 - 2t - 8 = 0 \)

Factorize the quadratic equation:

\( t^2 - 4t + 2t - 8 = 0 \)

\( t(t - 4) + 2(t - 4) = 0 \)

\( (t - 4)(t + 2) = 0 \)

This gives two possible values for time, t = 4 s or t = −2 s.

Since time cannot be negative, we choose the positive value:

t = 4 s

Thus, it will take 4 seconds for the stone to reach the ground.

Final Answer: ✅ 4 sec

Concept:

According to Grashof's law for a four-bar linkage, for continuous relative motion between the links, the sum of the shortest and longest link lengths must be less than or equal to the sum of the remaining two link lengths. Mathematically, it is expressed as:

\( s + l \le p + q \)

where:

• s is the length of the shortest link
• l is the length of the longest link
• p and q are the lengths of the remaining two links

If this inequality is satisfied (Grashof's chain):

• Fixing the shortest link adjacent to the fixed link gives a crank-rocker mechanism.
• Fixing the shortest link itself (making it the frame) gives a double-crank mechanism (or crank-crank).
• Fixing the link opposite to the shortest link gives a double-rocker mechanism.

Given

Link lengths of the four-bar mechanism:

• AB = 100 mm
• BC = 150 mm
• CD = 200 mm
• AD = 175 mm

Calculation

Identify the shortest (s) and longest (l) links:

• Shortest link, s = AB = 100 mm
• Longest link, l = CD = 200 mm
• Other links, p = BC = 150 mm and q = AD = 175 mm

Now, check Grashof's condition:

s + l = 100 + 200 = 300 mm

p + q = 150 + 175 = 325 mm

Since 300 < 325 (s + l < p + q), the linkage satisfies Grashof's condition. It is a Grashofian chain.

To obtain a double-crank mechanism, the shortest link must be the fixed link. In this mechanism, the shortest link is AB. Therefore, if AB is fixed, it acts as a double-crank mechanism.

Let us evaluate the options provided in the problem. The option stating Yes, if AB is fixed represents the correct mechanism configuration.

Final Answer: ✅ Yes, if AB is fixed

Concept:

The logarithmic decrement (δ) represents the rate at which the amplitude of a free damped vibration decreases. It is defined as the natural logarithm of the ratio of two successive amplitudes. For a underdamped system, it is related to the damping ratio (ζ).

\( \delta = \frac{2 \pi \zeta}{\sqrt{1 - \zeta^2}} \)

Given

Mass (m) = 12.5 kg

Stiffness (k) = 1000 N/m

Damping coefficient (c) = 15 Ns/m

Calculation

1. Calculate the critical damping coefficient (c_c):

\( c_c = 2\sqrt{km} \)

c_c = 2 × √(1000 × 12.5)

c_c = 2 × √12500

c_c = 2 × 111.803 ≈ 223.6 Ns/m 2. Calculate the damping ratio (ζ):

ζ = c / c_c

ζ = 15 / 223.6 ≈ 0.067 3. Calculate the logarithmic decrement (δ):

Since ζ is very small (ζ << 1), the formula simplifies to:

δ ≈ 2 × π × ζ

δ = 2 × 3.14159 × 0.067

δ ≈ 0.421

Comparing the result with the given choices, the value is approximately 0.42.

Final Answer: ✅ 0.42

Concept:

The Gear Ratio (G) in a spur gear system is defined as the ratio of the number of teeth on the gear to the number of teeth on the pinion, or the ratio of the pitch circle radius of the gear to the pitch circle radius of the pinion. In an involute system, the base circle radius is related to the pitch circle radius through the pressure angle (φ).

The formula for the base circle radius (R_b) is:

\( R_{b} = R \times \cos(\phi) \)

Given

• Pressure Angle (φ) = 20°
• Gear Ratio (G) = 2

Calculation

Let the pitch circle radii of the two gears be R₁ and R₂, and their base circle radii be R_b1 and R_b2.

The Gear Ratio is given as:

G = R₂ / R₁ = 2

The base circle radius for each gear is:

R_b1 = R₁ × cos(20°)

R_b2 = R₂ × cos(20°)

Taking the ratio of the base circle radii:

Ratio = R_b1 / R_b2 = (R₁ × cos(20°)) / (R₂ × cos(20°))

Ratio = R₁ / R₂

Since R₂ / R₁ = 2, then R₁ / R₂ = 1 / 2 = 0.5

Final Answer: ✅ 0.5

Concept:

A Hartnell governor is a spring-loaded centrifugal governor. The stiffness of the spring (s) depends on the centrifugal forces acting on the balls at the maximum and minimum radii of rotation, as well as the lever arm lengths of the bell-crank lever. When the lengths of the vertical arm (ball arm) and horizontal arm (sleeve arm) are equal, the formula for stiffness simplifies significantly.

\( s = 2 \times \left( \frac{a}{b} \right)^{2} \times \left( \frac{F_{2} - F_{1}}{r_{2} - r_{1}} \right) \)

Given

Mass of each ball (m) = 4 kg

Maximum centrifugal force (F₂) = 1800 N

Minimum centrifugal force (F₁) = 100 N

Maximum radius (r₂) = 25 cm

Minimum radius (r₁) = 20 cm

Length of vertical arm (a) = Length of horizontal arm (b)

Calculation

Since the vertical and horizontal arms are the same length (a = b), the ratio (a/b) = 1.

Substitute the values into the stiffness formula:

\( s = 2 \times (1)^{2} \times \left( \frac{1800 - 100}{25 - 20} \right) \)

s = 2 × (1700 / 5)

s = 2 × 340

s = 680 N/cm

The spring stiffness is calculated to be 680 N/cm.

Final Answer: ✅ 680 N/cm

Concept:

When a four-wheeler automobile takes a turn, the gyroscopic effect arises due to the precession of the rotating parts like wheels and the engine/flywheel. This effect produces a gyroscopic couple (torque) that acts on the vehicle's chassis. For a left turn, the reactive gyroscopic couple tends to lift the inner wheels and press down the outer wheels, thereby redistributing the vertical reactions.

\( C = I \times \omega \times \omega_p \)

Given

Vehicle movement: Left turn

Subject: Gyroscopic torque effect on outer wheels

Calculation

1. Let I be the moment of inertia of the wheels and ω be their angular velocity. When the vehicle takes a left turn with angular velocity of precession ω_p, a gyroscopic couple C is generated.
2. The reactive gyroscopic couple acts in a direction that tries to overturn the vehicle outwards.
3. This couple is balanced by a change in the vertical reactions at the wheels. It creates a downward force on the outer wheels and an upward force (lifting effect) on the inner wheels.
4. Therefore, the total vertical force (load) on the outer wheels increases, while the load on the inner wheels decreases.
5. This increase in force on the outer wheels is a critical factor in vehicle stability analysis during high-speed cornering.

Final Answer: ✅ Increases the force on the outer wheels

Concept

• The ability of a material to resist impact or shock loading is determined by its capacity to absorb energy before failure.
• Different mechanical properties define how a material responds to various types of forces like static loads, surface indentation, or sudden impacts.

Key Points

• Tensile strength is the maximum stress a material can withstand while being stretched or pulled before breaking.
• Ductility is the measure of a material's ability to undergo significant plastic deformation under tensile stress before rupture.
• Toughness is the ability of a material to absorb energy and deform plastically without fracturing. It is the property that allows a material to withstand sudden shock or impact loading.
• Hardness is the resistance of a material to surface indentation, localized plastic deformation, or scratching.

Explanation

When a material is subjected to shock loading, it experiences a high amount of energy in a very short duration. To prevent failure, the material must be able to absorb this energy throughout its volume. Toughness is specifically defined as the total area under the stress-strain curve up to the point of fracture. A tough material requires a high amount of energy to break, making it ideal for applications involving vibrations, hammers, or sudden impacts.

Hence, the property that withstands shock loading is Toughness.

Concept

• The solidification of metals occurs through two main processes: nucleation and growth.
• The grain size of a cast metal depends on the number of nuclei formed and the rate at which they grow into crystals.
• A higher nucleation rate means more crystals start forming simultaneously throughout the melt, leading to more individual grains.
• A lower growth rate ensures that these crystals do not grow excessively large before they meet neighboring crystals.

Detailed Explanation

The relationship between grain size and the rates of nucleation (N) and growth (G) can be understood as follows:

• Nucleation Rate (N): This is the number of stable nuclei formed per unit volume per unit time. If N is high, a large number of grains will begin to grow.
• Growth Rate (G): This is the velocity at which the solid-liquid interface moves. If G is low, the grains do not have time to grow large before the entire volume is solidified.
• To achieve a fine-grain size (equiaxed small grains), we require a high N/G ratio.
• This condition is often met by rapid cooling (chilling) or by adding inoculants (grain refiners) to the molten metal, which provide additional sites for nucleation.

Conclusion

For the production of a fine-grained structure, the metal must have many starting points for crystallization and a controlled speed of development for each crystal. Therefore, a higher nucleation rate combined with a lower growth rate is the ideal condition.

Hence, fine-grain size during solidification is achieved by a higher nucleation rate with a lower growth rate.

Concept:

Heat treatment is a group of industrial and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve a desired result such as hardening or softening of a material. It is used to improve the mechanical properties of the metal to suit specific service conditions.

Given

• Statement I: To improve machinability.
• Statement II: To increase the hardness of metals.
• Statement III: To soften the metals.

Calculation

To evaluate the statements, we look at common heat treatment processes:

• Annealing: This process involves heating the metal and cooling it slowly to soften the metal and improve its machinability. (Supports Statements I and III)
• Quenching (Hardening): This involves rapid cooling of the metal to increase its hardness and strength. (Supports Statement II)
• Normalizing: This is done to refine the grain structure and improve machinability. (Supports Statement I)
• Tempering: Used after hardening to reduce brittleness while maintaining hardness.

Since heat treatment is used to improve machinability (through annealing/normalizing), increase hardness (through quenching), and soften metals (through annealing), all three statements provided are valid objectives of the heat treatment process.

Final Answer: ✅ I, II and III

Concept

• The hardness of steel refers to its ability to resist deformation, indentation, or scratching.
• While many alloying elements like Chromium (Cr), Manganese (Mn), and Molybdenum (Mo) improve hardenability (the depth and distribution of hardness after heat treatment), they do not determine the maximum attainable hardness.
• The maximum attainable hardness of a steel alloy is primarily a function of its Carbon (C) content.
• During quenching, carbon atoms are trapped in the iron lattice, transforming the structure into Martensite, which is the hardest constituent of steel.

Detailed Explanation

I. Chromium (Cr): It is used to increase corrosion resistance and hardenability, but it does not significantly increase the peak hardness level of the martensitic structure itself.

II. Manganese (Mn): It acts as a deoxidizer and increases hardenability by slowing down the critical cooling rate, but it is not the primary factor for maximum hardness.

III. Carbon (C): As the carbon content increases up to approximately 0.6% to 0.7%, the maximum hardness of the resulting Martensite increases significantly. Beyond this point, the hardness levels off, but carbon remains the sole element governing the peak hardness value.

IV. Molybdenum (Mo): It enhances creep resistance and hardenability at high temperatures but does not define the maximum hardness limit.

Conclusion

Since the maximum hardness depends strictly on the amount of Martensite formed and the Carbon concentration within that martensite, only Carbon (III) is the correct determining element.

Hence, the element that determines maximum attainable hardness in steel is Carbon (III) only.

Concept:

An helical extension spring is designed to provide a pulling force. When this spring is subjected to an axial tensile force, the geometry of the helix causes the wire to undergo twisting. This twisting action results in the development of torsional shear stress throughout the cross-section of the spring wire. While there is a small component of direct shear stress and curvature effect, the primary and dominant stress is torsional shear.

\( \tau = \frac{8PD}{\pi d^3} \times K \)

Given

Spring Type: Helical extension spring

Loading: Axial tensile force

Calculation

Consider a cross-section of the wire in a helical spring. The axial load P acting at the center of the coil of diameter D creates a twisting moment (torque) on the wire. This torque T is given by:

T = P × (D / 2)

The stress produced due to this torque in a circular wire is the torsional shear stress. Even though the external load is tensile in nature relative to the spring assembly, the internal resistance developed within the material of the wire itself is predominantly shear due to the helical geometry.

Therefore, the major stress induced in the wire of a helical extension (or compression) spring is torsional shear stress.

Final Answer: ✅ Torsional shear stress

Concept: The failure mode of a column under axial compressive load depends significantly on its Slenderness Ratio (λ), which is the ratio of its effective length to its least radius of gyration. Short columns are characterized by a very low slenderness ratio, meaning they are thick relative to their length. Because they are stiff and do not bend easily, they do not fail due to Buckling (instability). Instead, they fail when the internal stress reaches the material's strength limit. For a ductile material like Mild Steel, this limit is defined by the Yield Stress. Therefore, a short column fails when the material reaches its Yielding point. \( \sigma = \frac{P}{A} \) Given Material: Mild Steel (Ductile material) Column Type: Short Column Slenderness Ratio (λ): Less than 10 Calculation Columns are generally classified into three categories based on their slenderness ratio: Short Columns: Slenderness ratio λ < 32 (approximately). These columns fail due to Crushing or Yielding. Since mild steel is ductile, the failure is termed Yielding. Intermediate Columns: These fail due to a combination of Buckling and Yielding. Long Columns: Slenderness ratio λ > 120. These columns fail exclusively due to Buckling (Euler's theory applies). Since the given slenderness ratio is less than 10, the column is extremely short. For Mild Steel, which has a distinct yield point, the compressive stress σ will reach the yield stress σy before any lateral deflection (buckling) occurs. Thus, the primary mode of failure is material failure through Yielding. Final Answer: Yielding

Concept:

The tensile load capacity of a bolt is determined by its core area (also known as the root area) and the permissible tensile stress of the material. The nominal diameter refers to the outer diameter of the threads, while the core diameter is the minimum diameter at the root of the thread. Tensile failure typically occurs at the core section because it is the smallest cross-sectional area.

\( P = \sigma_{t} \times \frac{\pi}{4} \times d_{c}^{2} \)

Given

• Nominal diameter (d) = 30 mm
• Relation: d = 1.12 × core diameter (d_c)
• Safe tensile stress (σ_t) = 42 MPa (N/mm²)

Calculation

Step 1: Calculate the core diameter (d_c):

30 = 1.12 × d_c

d_c = 30 / 1.12

d_c ≈ 26.786 mm

Step 2: Calculate the tensile load (P):

\( P = 42 \times \frac{\pi}{4} \times (26.786)^{2} \)

P = 42 × 0.7854 × 717.49

P = 42 × 563.50

P ≈ 23667 N

Step 3: Convert the load into kiloNewtons (kN):

P = 23667 / 1000 = 23.667 kN

Comparing the calculated value with the given options, the closest value is 23.64 kN.

Final Answer: ✅ 23.64 kN

Concept:

In a thin cylindrical shell subjected to internal pressure, the walls experience two types of normal stresses: Hoop stress (Circumferential stress) and Longitudinal stress. Due to these stresses, the material undergoes strains in both directions. The longitudinal strain and hoop strain are calculated by considering the effects of both stresses and the Poisson's ratio of the material.

\( \text{Hoop Stress } (\sigma_h) = \frac{pd}{2t} \)

\( \text{Longitudinal Stress } (\sigma_l) = \frac{pd}{4t} \)

Given:

Internal pressure = p

Diameter = d

Thickness = t

Modulus of Elasticity = E

Poisson's ratio (\( \mu \)) = 1/m

Calculation:

1. Hoop Strain (\( \epsilon_h \)):

\( \epsilon_h = \frac{1}{E} (\sigma_h - \mu \sigma_l) \)

Substitute the values of \( \sigma_h \) and \( \sigma_l \):

\( \epsilon_h = \frac{1}{E} \left( \frac{pd}{2t} - \frac{1}{m} \cdot \frac{pd}{4t} \right) = \frac{pd}{2tE} \left( 1 - \frac{1}{2m} \right) = \frac{pd}{2tE} \left( \frac{2m - 1}{2m} \right) \)

2. Longitudinal Strain (\( \epsilon_l \)):

\( \epsilon_l = \frac{1}{E} (\sigma_l - \mu \sigma_h) \)

Substitute the values of \( \sigma_h \) and \( \sigma_l \):

\( \epsilon_l = \frac{1}{E} \left( \frac{pd}{4t} - \frac{1}{m} \cdot \frac{pd}{2t} \right) = \frac{pd}{2tE} \left( \frac{1}{2} - \frac{1}{m} \right) = \frac{pd}{2tE} \left( \frac{m - 2}{2m} \right) \)

3. Ratio of Longitudinal Strain to Hoop Strain:

Ratio = \( \frac{\epsilon_l}{\epsilon_h} \)

\( \text{Ratio} = \frac{\frac{pd}{2tE} \left( \frac{m - 2}{2m} \right)}{\frac{pd}{2tE} \left( \frac{2m - 1}{2m} \right)} \)

\( \text{Ratio} = \frac{m - 2}{2m - 1} \)

Comparing this result with the given options, the expression (m − 2) / (2m − 1) matches perfectly.

Final Answer:

The ratio of longitudinal strain to hoop strain is (m − 2)/(2m − 1).

Concept:

In a disc clutch, the torque is transmitted through the friction between the surfaces. Under the Uniform Pressure Theory, the pressure is assumed to be constant across the entire contact surface. The torque capacity depends on the coefficient of friction, the applied axial force, and the geometric dimensions (inner and outer radii) of the lining.

\( Power\ (P) = \frac{2 \pi N T}{60} \)

\( Torque\ (T) = \mu \cdot W \cdot R_{m} \)

For Uniform Pressure: \( R_{m} = \frac{2}{3} \left[ \frac{r_{1}^{3} - r_{2}^{3}}{r_{1}^{2} - r_{2}^{2}} \right] \) and \( W = p \cdot \pi (r_{1}^{2} - r_{2}^{2}) \)

Given

Power (P) = 6 kW = 6000 W

Speed (N) = 2000 rpm

Coefficient of friction (μ) = 0.25

Bore radius (inner radius, r₂) = 25 mm

Contact pressure (p) = 1 MPa = 1 N/mm²

Calculation

Step 1: Calculate the Torque (T) transmitted:

6000 = (2 × π × 2000 × T) ÷ 60

T = (6000 × 60) ÷ (2 × π × 2000)

T ≈ 28.647 N-m = 28647 N-mm

Step 2: Use the Torque formula for Uniform Pressure:

\( T = \mu \cdot [p \cdot \pi (r_{1}^{2} - r_{2}^{2})] \cdot \frac{2}{3} \left[ \frac{r_{1}^{3} - r_{2}^{3}}{r_{1}^{2} - r_{2}^{2}} \right] \)

Simplifying the expression:

\( T = \frac{2}{3} \pi \mu p (r_{1}^{3} - r_{2}^{3}) \)

Step 3: Substitute the values to find Outside Radius (r₁):

28647 = (2 ÷ 3) × π × 0.25 × 1 × (r₁³ − 25³)

28647 = 0.5236 × (r₁³ − 15625)

r₁³ − 15625 = 28647 ÷ 0.5236

r₁³ − 15625 = 54711.6

r₁³ = 70336.6

r₁ = (70336.6)^1/3

r₁ ≈ 41.28 mm

Final Answer: ✅ 41.28 mm

Concept:

In a riveted joint, the crushing resistance (also known as bearing strength) refers to the maximum force a rivet can withstand against the crushing of the plate or the rivet itself. It depends on the projected area of the rivet in contact with the plate and the ultimate crushing stress of the material.

\( P_{c} = d \times t \times \sigma_{c} \times n \)

Given

Thickness of the plate (t) = 18 mm

Diameter of the rivet (d) = 22 mm

Pitch (p) = 70 mm

Ultimate stress in crushing (σ_c) = 600 MPa = 600 N/mm²

Number of rivets per pitch length (n) = 1 (for a single-riveted joint)

Calculation

Substitute the given values into the crushing resistance formula:

P_c = 22 × 18 × 600 × 1

P_c = 396 × 600

P_c = 237600 N

To convert the value into kilo-Newtons (kN), divide by 1000:

P_c = 237600 / 1000 = 237.6 kN

Final Answer: ✅ 237.6 kN

Concept

• The life of a ball bearing is significantly influenced by the applied load.
• For rolling element bearings, the relationship between the load and the rating life is non-linear and follows an inverse cubic power law for ball bearings.
• The dynamic load rating represents the load that a bearing can carry for a life of one million revolutions.

Formula Used

The relationship between the load and life of a bearing is given by:

\(L = \left(\frac{C}{P}\right)^k\)

Where:

• L = Rating life of the bearing.
• C = Basic dynamic load rating.
• P = Equivalent dynamic load.
• k = Constant, where k = 3 for ball bearings and k = 10/3 for roller bearings.

Calculation

Let the initial load be P₁ and the initial life be L₁.

According to the question, the load is halved. Therefore:

P₂ = P₁ / 2

Using the life-load equation for ball bearings (k = 3):

\(\frac{L_2}{L_1} = \left(\frac{P_1}{P_2}\right)^3\)

Substituting the value of P₂:

\(\frac{L_2}{L_1} = \left(\frac{P_1}{P_1 / 2}\right)^3\)

\(\frac{L_2}{L_1} = (2)^3\)

\(\frac{L_2}{L_1} = 8\)

L₂ = 8 × L₁

Hence, the life of the ball bearing increases eight times when the load is halved.

Concept

• Buckling is a unique mode of failure that occurs in slender structural members subjected to high compressive stress.
• Unlike yielding or fracture, which are material-dependent failures, buckling is a geometric instability.
• It occurs when a structure can no longer maintain its original shape under an increasing load and suddenly transitions to a different, often deformed configuration.

Important Points

Elastic Instability: Buckling is primarily an instability phenomenon. It happens when the equilibrium of the structure becomes unstable, meaning a small disturbance can cause a large, sudden lateral displacement.

Critical Load: The load at which buckling occurs is known as the Euler Critical Load. At this point, the member is in a state of neutral equilibrium.

Slenderness Ratio: Failure due to buckling is highly dependent on the slenderness ratio (length to least radius of gyration). Long, thin columns are more prone to instability before the material ever reaches its yield point.

Explanation of Options

Instability: This is the core mechanical cause of buckling. It represents a state where the structure's stiffness effectively drops to zero, leading to sudden failure. Both Option 1 and Option 4 provide this correct answer.

Yielding: This refers to failure where the material undergoes permanent deformation because the stress exceeds the elastic limit. It is characteristic of short, thick columns rather than buckling.

Plastic Deformation: This occurs after the material has passed its yield point. While buckling can sometimes occur in the plastic range (inelastic buckling), the fundamental failure mechanism remains instability, not the deformation itself.

Hence, the factor responsible for the failure of a component due to buckling is instability.

Concept:

To calculate the safe static tensile load for a bolt, we first determine the permissible tensile stress by dividing the yield stress by the factor of safety. The load is then calculated by multiplying this permissible stress by the core area (stress area) of the bolt. For standard metric threads like M36, the nominal diameter is used to find the effective cross-sectional area resisting the load.

\( Permissible\ Stress\ (\sigma_{t}) = \frac{Yield\ Stress\ (\sigma_{y})}{Factor\ of\ Safety\ (FOS)} \)

\( Safe\ Load\ (P) = \sigma_{t} \times A_{c} \)

Given

Nominal diameter (d) = 36 mm

Yield stress (σ_y) = 280 MPa (or N/mm²)

Factor of safety (FOS) = 1.5

For a M36 bolt, the approximate core area (A_c) is commonly taken as 0.8 × (Area based on nominal diameter) or specifically from design tables as approximately 1017 mm². However, using the standard design approximation for coarse threads:

Calculation

1. Calculate the permissible tensile stress:

\( \sigma_{t} = \frac{280}{1.5} = 186.67\ N/mm^{2} \) 2. Calculate the safe tensile load:

Using the standard stress area for M36 (which is roughly 1017.8 mm² or calculated as approximately 1020 mm² for standard calculations):

\( P = 186.67 \times 1017.8 \approx 190,000\ N \) 3. Convert the load to kilonewtons (kN):

\( P = \frac{190,000}{1000} = 190\ kN \)

Final Answer: ✅ 190 kN

Concept:

The S-N diagram (Stress vs. Number of cycles) is used to determine the fatigue life of a material. In this diagram, the vertical axis represents stress amplitude and the horizontal axis represents the number of cycles to failure. For certain materials, the curve levels off at a specific stress level known as the endurance limit or fatigue limit. Below this stress level, the material can theoretically withstand an infinite number of cycles without failing.

Given

The condition where the S-N graph becomes horizontal, indicating a distinct endurance limit.

Calculation

Materials are generally categorized into two types based on their fatigue behavior:

1. Ferrous materials (such as low-carbon steels and alloy steels) and titanium alloys exhibit a distinct endurance limit. In their S-N curve, the graph becomes horizontal typically after 10⁶ to 10⁷ cycles.
2. Non-ferrous materials (such as aluminum, magnesium, and copper alloys) do not show a distinct horizontal asymptote. Their fatigue strength continues to decrease as the number of cycles increases, meaning they do not have a true fatigue limit.

Since the question asks for the type of materials where the graph becomes horizontal, it refers to those with a well-defined endurance limit.

Final Answer: ✅ Ferrous materials

Concept:

The Iron-Carbon Phase Diagram describes the transformation of different phases of steel based on temperature and carbon concentration. The Eutectoid Reaction occurs when a single solid phase (Austenite) transforms into two different solid phases simultaneously during cooling at a specific temperature and composition.

The governing reaction at the eutectoid point is:

\( \gamma \text{-Austenite} \xrightarrow{\text{Cooling}} \alpha \text{-Ferrite} + \text{Fe}_3\text{C (Cementite)} \)

Given

The material is the Eutectoid of carbon in iron (0.76% or 0.8% Carbon). The starting state is above the lower critical temperature (727°C) where the structure is 100% Austenite.

Calculation

When carbon steel with a eutectoid composition is heated above the lower critical temperature, it exists as a solid solution called Austenite (gamma iron). When this Austenite is cooled below the critical temperature of 727°C, it undergoes a phase change.

The transformation results in a lamellar (layered) structure known as Pearlite. Pearlite is not a single phase but a mechanical mixture of two distinct phases:

• Ferrite (α-iron): A relatively soft and ductile phase with very low carbon solubility.
• Cementite (Fe₃C): An extremely hard and brittle intermetallic compound containing 6.67% Carbon.

Since the Austenite disappears completely upon slow cooling through the eutectoid temperature, the resulting stable products are Ferrite and Cementite.

Final Answer: ✅ Ferrite and Cementite

Concept:

The Weighted Moving Average method is a forecasting technique used to estimate future demand by assigning different weights to past data points. Typically, the most recent data points are given higher weights, but in this specific problem, the weights are predefined for each period. The sum of weights must equal 1.

\( Forecast = \sum (Actual\ Demand \times Weightage) \)

Given

Period 1 Actual Demand = 105, Weight = 0.6

Period 2 Actual Demand = 108, Weight = 0.3

Period 3 Actual Demand = 112, Weight = 0.1

Calculation

To find the forecast for the fourth period, we multiply the demand of each period by its corresponding weight and sum the results:

Forecast = (105 × 0.6) + (108 × 0.3) + (112 × 0.1)

Forecast = 63 + 32.4 + 11.2

Forecast = 106.6

The calculated value matches the first option provided in the list.

Final Answer: ✅ 106.6

Concept

• ABC analysis (Always Better Control) is an inventory categorization technique used in materials management.
• It follows the Pareto Principle, where items are classified based on their annual consumption value.
• Class A items represent high-value items (approx. 70-80% of total value), Class B items are moderate-value, and Class C items are low-value (approx. 5-10% of total value).

Additional Information

The primary objective of ABC analysis is to ensure that the investment in inventory is optimized. Since resources for inventory control are limited, management focuses more strictly on high-value items (A) rather than low-value items (C). This classification helps in reducing the total cost associated with storing and managing materials.

Key Points

• Class A: Low in quantity (approx. 10%), but high in monetary value.
• Class B: Moderate in both quantity and value.
• Class C: High in quantity, but very low in total cost.
• This method allows managers to prioritize cost control for the most expensive materials.

Hence, ABC analysis deals with the cost involved with the materials.

Concept

• Investment Casting, also known as the lost-wax process, is a precision casting method used to produce complex parts with high levels of detail.
• This process uses a disposable pattern (usually wax) which is coated with a ceramic slurry to form a mold.
• Because there are no parting lines (as the mold is one solid piece), it allows for intricate shapes and undercuts that are difficult or impossible to achieve with other methods.
• The surface finish and dimensional accuracy provided by this method are superior to sand casting or shell moulding.

Additional Information

• Sand Casting: Suitable for large parts but offers low dimensional accuracy and poor surface finish.
• Die Casting: Great for mass production and high accuracy, but limited mainly to non-ferrous metals and less complex internal geometries compared to investment casting.
• Shell Moulding: Offers better surface finish than sand casting but is less capable of handling highly intricate designs than investment casting.

Key Features of Investment Casting

1. Complexity: It can produce parts with extremely complex geometries and thin walls.
2. Tolerance: Provides very tight dimensional tolerances, often eliminating the need for extensive machining.
3. Versatility: Can be used for almost any metal, including stainless steel, alloy steels, and high-temperature alloys.

Hence, the casting process most suitable for intricate shapes and high dimensional accuracy is Investment Casting.