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Correct answer: 1) 200 Newtons

Key Points

• The question states that a force of 200 Newtons is applied to push a wooden box at constant velocity. According to Newton's First Law and the concept of dynamic (kinetic) friction, if an object is moving at constant velocity, the net force on it must be zero.
• This means the applied force is exactly balanced by the frictional force.
• So, the marginal friction force (which is the kinetic friction opposing motion) must also be 200 Newtons.

Correct Answer: 14,000 N

A truck starts from rest and moves 400 m in 20 s. Its mass is 7 tonnes = 7000 kg. We first find the acceleration and then apply Newton’s second law for the force.

Kinematics (from rest): s = ut + ½ a t², with u = 0

⇒ 400 = ½ × a × 20²

⇒ 400 = 200a

⇒ a = 2 m/s²

Now, Newton’s second law: F = m × a

⇒ F = 7000 × 2 = 14,000 N

Thus, the required force to produce this motion is 14,000 Newtons. The result is consistent with uniform acceleration from rest over the stated distance and time.

The Correct answer: 3) 9 × 10⁸

Key PointsTo solve this, we need to convert energy units (kWh) to joules.

 Given:

• Energy consumed = 250 units
• 1 unit of electricity = 1 kilowatt-hour (kWh)
• 1 kWh = 3.6 × 10⁶ joules

 

Step 1: Understand "Units"

• In electricity billing, 1 unit = 1 kilowatt-hour (kWh)
• So, 250 units = 250 kWh

Step 2: Convert kWh to Joules

We use the conversion:

1 kWh=3.6×106 Joules1 , $\text{kWh} = 3.6 \times 10^6 , \text{Joules}1$kWh=3.6×106Joules

So,

250 kWh=250×3.6×106=900×106=9×108 Joules250 , $\text{kWh} = 250 \times 3.6 \times 10^6 = 900 \times 10^6 = 9 \times 10^8 , \text{Joules}250$kWh=250×3.6×106=900×106=9×108Joules

Correct Answer: 3) 9×1089 $\times 10^89$×108

The speed of sound is maximum in solids, then liquids, and minimum in gases.

Typical values:

• Steel: ~5000 m/s
• Water: ~1500 m/s
• Air: ~343 m/s
• Hydrogen: ~1284 m/s

Additional Information

What affects the speed of sound?

The speed of sound in any medium depends on two main physical properties:

• Elasticity (how easily the medium returns to its original shape after deformation)
• Density (mass per unit volume)

The general formula for the speed of sound is:

v=Eρ−−√v=Eρ $v = \sqrt{\frac{E}{\rho}}$

v=ρE​

Where:

• vv v

v = speed of sound

• EE E

E = modulus of elasticity (bulk modulus or Young's modulus depending on the medium)

• ρρ $\rho$

ρ = density of the medium

• How it works across different states of matter:

1. Solids (like steel):

• Very high elasticity
• Molecules are tightly packed, so they transmit vibrations quickly
• Speed is highest

2. Liquids (like water):

• Less elastic than solids, but still better than gases
• Speed is moderate

3. Gases (like air, hydrogen):

• Low elasticity and loosely packed molecules
• Speed is slowest

Speed of Sound in Different Media (approximate values):

Why not hydrogen?

• While hydrogen has a lower density than air and the speed of sound is faster in hydrogen than in air, it's still much slower than in solids like steel.

The Correct Answer: 1) The principle of conservation of energy is not violated

 

Key Points When a body falls freely under gravity, here's what happens:

1. At the top:

• It has maximum potential energy (PE).
• Kinetic energy (KE) is zero (if starting from rest).

2. As it falls:

• Height decreases, so potential energy decreases.
• But at the same time, speed increases, so kinetic energy increases.

3. Total mechanical energy remains constant:

 

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=ConstantTotal Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant $\text{Total Energy} = \text{Potential Energy (PE)} + \text{Kinetic Energy (KE)} = \text{Constant}$

Total Energy=Potential Energy (PE)+Kinetic Energy (KE)=Constant

Energy Transformation:

Conservation of Energy Principle:

It states that energy can neither be created nor destroyed, only transformed from one form to another.

In this case:

• Potential energy is converted into kinetic energy, so total energy is conserved.

The Correct Answer is 2100 Joule

Key PointsWe are given:

• Force (F) = 140 Newton
• Distance (d) = 15 meters
• We need to find the Work Done (W)

Formula for Work Done:

Work Done (W)=Force (F)×Distance (d)Work Done (W)=Force (F)×Distance (d) $\text{Work Done (W)} = \text{Force (F)} \times \text{Distance (d)}$

Work Done (W)=Force (F)×Distance (d)

Substitute the values:

 

W=140×15=2100 JouleW=140×15=2100 Joule W = 140 $\times 15 = 2100 , \text{Joule}$

W=140×15=2100Joule Therefore, the correct answer is: 2100 Joule.

The Correct Answer is Option 4) Infinity (∞)

Key Points

What is focal length?

The focal length of a mirror is the distance between its pole (geometric center) and the focus — the point where parallel rays either converge (concave mirror) or appear to diverge from (convex mirror).

For a plane mirror:

• A plane mirror is perfectly flat and has no curvature.
• It does not converge or diverge the incident light rays.
• Hence, it has no real focus like spherical mirrors do.
• For this reason, its focal length is taken to be infinity (∞).

Formula Insight:

For spherical mirrors, the relation between focal length and radius of curvature is:

f = R / 2

where R is the radius of curvature of the mirror.

For a plane mirror, the reflecting surface is not curved, so R = ∞.

⇒ f = R / 2 = ∞ / 2 = ∞

Conclusion:

The focal distance of a plane mirror is infinite because it has no curvature to focus light rays.

So, the correct answer is: 4) Infinity.

The correct answer is IR².

Key Points

• Electric power in a circuit is defined as the rate at which electrical energy is consumed or converted into another form of energy, such as heat or light.
• The formula for electric power is given by P = VI, where V is the voltage across the circuit and I is the current flowing through it.
• Using Ohm's law, V = IR, the power can also be expressed as P = I²R or P = V²/R, where R is the resistance of the circuit.
• The correct formulas that denote electric power are P = I²R, P = VI, and P = V²/R. These are derived directly from the fundamental definitions and laws of electricity. Hence, the correct answer is IR².

Additional Information

• Electric Power Formulas:
• P = VI: This is the most basic formula for electric power, where power is directly proportional to the product of voltage and current.
• P = I²R: This formula is derived from Ohm's law and represents the power dissipated as heat in a resistive circuit.
• P = V²/R: This is another derived formula, which shows the power in terms of voltage and resistance.
• Applications of Electric Power:
• Industrial Use: Power calculation is essential for designing electrical machinery like transformers, motors, and generators.
• Domestic Use: Power ratings of household appliances, such as heaters, air conditioners, and bulbs, are determined using these formulas.
• Electricity Billing: Power consumption is measured in kilowatt-hours (kWh), where the power formula is used to calculate energy usage.
• Important Observations:
• Dimensional Analysis: The term IR² is dimensionally inconsistent with power, which is measured in watts (Joules per second).
• Correct Usage: Only terms derived from the basic formula P = VI can represent electric power.

Important Points

• Ohm's Law:
• Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, expressed as V = IR.
• This law is fundamental in deriving different formulas for electric power.
• Units and Dimensions of Power:
• Unit of Power: The SI unit of electric power is the watt (W), where 1 watt = 1 Joule/second.
• Dimensional Formula: The dimensional formula for power is ML²T⁻³.

The Correct Answer is Option 3

Key Points What is a short circuit?

A short circuit occurs when a low-resistance path is created unintentionally in an electric circuit, allowing current to bypass the intended load (like a bulb, resistor, etc.).

What happens in a short circuit?

According to Ohm’s Law:

I=VR$I = \frac{V}{R}I=$RV​

Where:

• III = Current
• VVV = Voltage
• RRR = Resistance

 In a short circuit, the resistance RRR becomes very small (almost zero).

I=Vvery small number⇒I→very large$I = \frac{V}{\text{very small number}} \Rightarrow I \rightarrow \text{very large}I=$very small numberV​⇒I→very large

So, the electric current increases to a very high value.

Why is this dangerous?

• Excessive current can cause overheating, fires, or damage to electrical components.
• That’s why fuses and circuit breakers are used — to break the circuit in such situations.

Conclusion: In a short circuit, current increases to a very high value due to negligible resistance.

So, the correct answer is: 3) Increases very high.

The Correct Answer is Option 2

Key Points What is a fuse?

A fuse is a safety device used in electrical circuits to protect appliances and humans from damage or electric shock due to excess current.

How does it work?

• A fuse contains a thin wire made of a metal with a low melting point.
• When the current exceeds a safe limit, the wire heats up and melts.
• This breaks the circuit, stopping the flow of electricity and preventing:
• Equipment damage
• Electric shock
• Fire hazards

Why the other options are incorrect:

• 1) Generator – Produces electricity, not for protection
• 3) Motor – Converts electrical energy into mechanical energy
• 4) Current controller – Regulates current but doesn’t protect from shocks

Conclusion:

A fuse is specifically designed to protect equipment and users by breaking the circuit during overload or fault conditions.