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QUESTION: 1

An Indian rubber cube of side 10 cm has one side fixed while a tangential force of 1800 N is applied to the opposite side. Find the shear strain produced. Take η = 2 x 10^{6} N/ m^{2}.

Solution:

QUESTION: 2

The length of the wire is increased by 1 mm on the application of a given load. In a wire of the same material but of length and radius twice that of the first, on application of the same force, extension produced is

Solution:

Young's Modulus of elasticity =stress/strain

Y= [F/a/△l/l] or Y= [Fl/a△l]

or △l= [Fl/aY] = Fl/ πr^{2}Y

In the given problem, △l∝ l/ r^{2}

When both l and r are doubled, △l is halved.

QUESTION: 3

Young’s modulus is defined as the ratio of longitudinal stress to longitudinal strain. Which of the following is the unit of Young’s modulus?

Solution:

Stress = Force per area and strain is unit less.

Therefore in CGS units dyne per cm square.

Hence A is correct.

QUESTION: 4

The volume of a spherical body is decreased by 10^{-3}% when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body.

(1 atm = 1.01 x 10^{3} N/m^{2}).

Solution:

We know that magnitude of bulk modulus

K=[P/(dV/V)]

Now, percentage change in volume is. 10^{-3} %

Therefore, (dV/V)x100=10^{-3}

So, dV/V=10^{-5}

Hence, k is,

K=40atm/10^{-5}=40x1.01x10^{5} /10^{-5} =4.04x10^{11} N/m^{2 }

QUESTION: 5

The materials which have the same elastic properties in all directions are called __________.

Solution:

Same elastic properties in all direction is called the homogenity of a material.

QUESTION: 6

How does the modulus of elasticity change with temperature?

Solution:

As the temperature increases, the inter-atomic distance also increases. So, it results in an increase in the area (stress = force /area). As the area increases stress decreases, this results in a decrease in Young's modulus.

QUESTION: 7

What type of stress is produced in a body when the deforming force produces sheer strain?

Solution:

When the direction of the deforming force or external force is parallel to the cross-sectional area, the stress experienced by the object is called shearing stress or tangential stress. This results in the change in the shape of the body.

QUESTION: 8

Modulus of rigidity is defined as the

Solution:

Modulus of rigidity is defined as the ratio of Shear stress to shear strain.

QUESTION: 9

Which of the following represents Hooke’s Law?

Solution:

E=stress/strain

Strain x E= Stress

QUESTION: 10

An iron bar of length l cm and cross section A cm^{2} is pulled by a force F dynes from the ends so as to produce an elongation l cm. Which of the following statements is correct?

Solution:

F =AYΔl/L

Δl = FL/AY

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