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Explanation:

Center of Gravity

• The force of attraction, which is proportional to the mass of the particle, acts vertically downwards and is known as the weight of the body.
• As the distance between the different particles of a body and the center of the earth is taken as the same, therefore these forces may be taken to act along parallel lines.
• A point may be found out in a body, through which the resultant of all such parallel forces act.
• This point, through which the whole weight of the body acts is known as the Center of gravity.

Centroid

• The plane figures (triangle, quadrilateral, circle, etc) have only areas, but no mass. The center of the area of plane figures is known as Centrold.

Concept:

When two or more forces act on a body, they are called to form a system of forces.

Coplanar forces: The forces, whose lines of action lie on the same plane, are known as coplanar forces.

Collinear forces: The forces, whose lines of action lie on the same line, are known as collinear forces.

Concurrent forces: The forces, which meet at one point, are known as concurrent forces. The concurrent forces may or may not be collinear.

Coplanar concurrent forces: The forces, which meet at one point and their lines of action also lie on the same plane, are known as coplanar concurrent forces.

Coplanar non-concurrent forces: The forces, which do not meet at one point, but their lines of action lie on the same plane, are known as coplanar non-concurrent forces.

Non-coplanar concurrent forces: The forces, which meet at one point, but their lines of action do not lie on the same plane, are known as non-coplanar concurrent forces.

Non-coplanar non-concurrent forces: The forces, which do not meet at one point and their lines of action do not lie on the same plane, are called non-coplanar non-concurrent forces.

Explanation:

Fine-Grained Soil:

• The majority of the fine-grained soils are physico-chemically active, which can be attributed to their unbalanced surface charges.
• Some of the undesirable properties of these soils such as high swell-shrink potential, high compressibility, low permeability, low strength and low CBR are essentially due to the surface charges of fine-grained soils.
• These surface charges favour the development of a diffuse double layer, which in turn can be taken to contribute to the water-holding capacity of soils. As a consequence of this, the volume stability of the soils gets adversely affected; effective voids volume gets reduced which is responsible for the low permeability of such soil: actual void ratio becomes more than the theoretical which is responsible for higher compressibility, double layer repulsion increases which is responsible for the lower effective stress and hence, for lesser strength.

Explanation: 

• Evaporation is one of the cause of water losses.
• Runoff is the quantity of water that discharge in surface stream.
• Percolation is the downward movement of soil also called infiltration of soil. Percolation do not cause soil erosion.
• Storm is a violent disturbance of atmosphere with strong wind, rain, thunder, lightning or snow.

Explanation

In IS 456:2000 Clause 26, requirements related to reinforcement used in RCC are given below.

Explanation:

The pressure in a fluid is measured in two different systems.

1. In the first system, it is measured above the absolute zero or zero vacuum which is termed as Absolute pressure.
2. In the second system, Pressure is measured above the atmospheric pressure, it is known as Gauge Pressure.

• ​​Gauge Pressure is measured after taking atmospheric pressure as a datum, i.e. atmospheric pressure is marked as zero.
• Thus it can be concluded that on the gauge pressure is relative to local atmospheric pressure.

Mathematically, it can be represented as:

Absolute Pressure = Atmospheric pressure + Gauge Pressure

Therefore, Gauge Pressure = Absolute Pressure - Atmospheric pressure

CONCEPT:

• Weight of the body (W): It is defined as the force acting on a body due to gravity.

The weight of a body is calculated by the formula:

W = mg

where W is the weight of the body, m is the mass of the body, and g is the gravitational acceleration.

EXPLANATION:

From the definition, the weight of the body at a place is given by W = mg

g₁ is the acceleration due to gravity when weight is W₁

g₂ is the acceleration due to gravity when weight is W₂

According to the given condition in question, g₂ = 2g₁

Mass remains the same, So

M₁ = M₂

\({{W_1\over g_1}} = {W_2 \over g_2}\)

\({{W_1\over g_1}} = {W_2 \over2g_1}\)

W₂ = 2 × W₁

Concept:

Methods of finding resultant of forces

A) Law of a parallelogram of forces

Where P and Q are two forces acting on a body with angle θ between them

α = Angle made by resultant with respect to force P

α is the direction of resultant R

\({\rm{R}} = \sqrt {{{\rm{P}}^2} + {{\rm{Q}}^2} + 2{\rm{PQ}}\cos {\rm{\theta }}} \)

\({\rm{\alpha }} = {\tan ^{ - 1}}\left[ {\frac{{{\rm{Q}}\sin {\rm{\theta }}}}{{{\rm{P}} + {\rm{Q}}\cos {\rm{\theta }}}}} \right]{\rm{;;}}\)

B) Method of resolution of forces

ΣFX = summation of forces acting in X-direction

ΣFY = Summation of forces acting in Y-direction

\({\rm{R}} = \sqrt {{{\left( {{\rm{\Sigma }}{{\rm{F}}_{\rm{X}}}} \right)}^2} + {{\left( {{\rm{\Sigma }}{{\rm{F}}_{\rm{Y}}}} \right)}^2}} \)

\({\rm{\theta }} = {\tan ^{ - 1}}\left| {\frac{{{\rm{\Sigma }}{{\rm{F}}_{\rm{Y}}}}}{{{\rm{\Sigma }}{{\rm{F}}_{\rm{X}}}}}} \right|\)

Calculation:

Let the force P = 6 Nt and Q = 8 Nt and θ = 90°

By law of parallelogram of forces

\({\rm{R}} = \sqrt {{{\rm{P}}^2} + {{\rm{Q}}^2} + 2{\rm{PQ}}\cos {\rm{\theta }}} \)

\({\rm{R}} = \sqrt {{6^2} + {{8}^2} + 2 \times 6 \times 8 \times \cos 90^\circ } \)

\({\rm{R}} = \sqrt {{6^2} + {{8}^2}} \)

R = 10 Nt

Explanation: 

When the bar is subjected to compressive force P (Push), it gets compressed but due to Poisson's effect its width and thickness increase. 

Poisson's effect:

• When a material is elongated in one direction, it tends to compress in the perpendicular direction of loading and vice-versa. This phenomenon is known as Poisson's effect. The measure of Poisson's effect is given in terms of Poisson's ratio.

​

Poisson's ratio: 

Poisson's ratio is defined as the ratio of Transverse strain to Longitudinal strain, as the Transverse strain is always opposite in nature to longitudinal strain thus negative sign is used.

Poisson ratio \(\mu= -\frac{Lateral strain}{Longitudinal strain} = -\frac{\epsilon _{y}}{\epsilon _{x}}= -\frac{\epsilon _{z}}{\epsilon _{x}}\)

Where \(\epsilon _{x}\) = Longitudinal strain in the direction of loading,

            \(\epsilon _{y}\)  and \(\epsilon_{z}\) = Lateral strain in the perpendicular direction of loading.

For most materials,Value of the Poisson ratio lies between 0 to 0.5 

Thus if a bar of length (I), breadth (b), and thickness (t) is subjected to a push of (P) kg, its Length decreases, and Width and Thickness increase.

Additional Information

Explanation:

• The distance between the inner sides of two tracks on any railway line is called Railway Guage.
• There are 4 types of railway gauges used in India: Broad gauge, Metre Gauge, Narrow gauge, and Standard gauge.

Broad gauge:

• It is often called a wide gauge.
• The distance between the two tracks in these railway gauges or the width of the broad gauge used in the Indian railway track is 1676 mm or 1.676 m.

Standard gauge:

• The width of the standard gauge used in the Indian railway track is 1435 mm.

Metre Gauge:

• The width of the Metre gauge used in the Indian railway track is 1000 mm.

Narrow Gauge:

• It is often called a small gauge.
• The width of the narrow gauge used in the Indian railway track is 762 mm and 610 mm.