Mechanical properties of solids practice · Mixed difficulty

Assertion: Two wires $A$ and $B$ have the same cross-sectional area and are made of the same material but the length of wire $A$ is twice that of $B$. For a given load, the strain in wire $A$ is twice that in $B$.
Reason: For a given load, the extension in a wire is not proportional to its length.

In magnitude hydraulic stress is equal to:

Assertion(A): Bulk modulus of an incompressible fluid is infinite.

Reason(R): Density of incompressible fluid remains constant.

The Marina trench is located in the Pacific Ocean and at one place it is nearly eleven $\mathrm{km}$ beneath the surface of water. The water pressure at the bottom of the trench is about $1.1 \times 10^8 \mathrm{~Pa}$. A steel ball of initial volume $0.32 \mathrm{~m}^3$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?

Assertion(A): Upto the elastic limit, strain $\propto$ stress.

Reason(R): Upto elastic limit, material returns to its original shape and size, when external force is removed.

Assertion:- Elastic restoring forces may be conservative
Reason:- The value of strain for same stress are different while increasing the load and while decreasing the load.

The area of cross section of a steel wire $\left( {Y = 2.0\,\, \times {{10}^{11}}\,N/{m^2}} \right)$ is $0.1\,\,c{m^2}$. The force required to double its length will be

Consider the two statements.

I. Mach number is the ratio of strain to stress.

II. Sound waves in air are longitudinal while light waves in air are transverse.

Choose the correct option among the following.

When a spring is stretched by a distance $x$ , it exerts a force given by $F = \left[ { - 5x - 16{x^3}} \right]N$.
The work done, when the spring is stretched from $0.1\,\,m\,\,\mathrm{to}\,\,0.2\,\,m$ is

Statement I: Strain is a unitless quantity.
Statement II: Strain is equivalent to force.

Which of the following statements is correct?

If the area of cross-section is halved and length of wire having young's modulus $Y$ is doubled, then its young's modulus will become

An elastic material of Young’s modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

What is the Young's modulus of elasticity for a perfectly rigid body?

The pressure of a medium is changed from $1.01 \times {10^5}$ Pa to $1.165\,\, \times {10^5}$ Pa and change in volume is $10\,\,\%$ keeping temperature constant. The Bulk modulus of the medium is

Statement I: A hollow shaft is found to be stronger than a solid shaft made of same material.
Statement II: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

A: Diamond is more elastic than rubber.
R: When same deforming force is applied diamond deforms less than rubber.

A mass of $100 \mathrm{~gram}$ is attached to the end of a rubber string $49 \mathrm{~cm}$ long and having an area of cross-section $20 \mathrm{~mm}^2$. The string is whirled round, horizontally at a constant speed of $40 \mathrm{~rps}$ in a circle of radius $51 \mathrm{~cm}$. Find Young's modulus of rubber.

A wire of length L and cross-section A is made of material of Young’s modulus Y. It is stretched by an amount x, the work done is

A metal rod of Young’s modulus $2 \times {10^{10}}\,N{m^{ - 2}}$ undergoes an elastic strain of $0.2\%$. The energy per unit volume stored in the rod in $joule/{m^3}$ is

Cross sectional area of a wire $\left(\mathrm{Y}=5 \times 10^{11}\right.$ $\mathrm{N} / \mathrm{m}^2$ ) is $0.1 \mathrm{~cm}^2$. Find the force required to make its length double.

With rise in temperature, the Young’s modulus of elasticity:

A $14.5 \mathrm{~kg}$ mass, fastened to the end of a steel wire of unstretched length $1 \mathrm{~m}$, is whirled in a vertical circle with an angular velocity of $2 \mathrm{~rev} / \mathrm{s}$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \mathrm{~cm}^2$. The elongation of the wire when the mass is at the lowest point of its path is;

$\text {[ } Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2 \text { ] }$

When a force is applied at one end of an elastic wire, it produces a strain $E$ in the wire. If $Y$ is the Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

A wire increases by $10^{-3}$ of its length when a stress of $1 \times 10^8 \mathrm{~Nm}^{-2}$ is applied to it. What is the Young's modulus of the material of the wire?