Mechanical properties of solids practice · Mixed difficulty

If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of the force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus for copper may be taken equal to that of iron) is

The relation between $Y, G$, and $B$ is:

For most of the material, Young's modulus $(Y)$ and rigidity modulus $(G)$ are related as

Under elastic limit the stress is

Energy stored in stretching a string per unit volume is

The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the following statement(s) is/are correct?

A rod elongated by $l$ when a body of mass $M$ is suspended from it. The work done is

A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is

A: Bulk modulus for a perfectly plastic body is zero.
R: For perfect plastic material, there is no restoring force.

The work done in deforming body is given by

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

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

A: It is the breaking stress and not the breaking strength which depends on the material
R: Breaking strength $=\frac{\text {Breaking stress}}{\text {Area}}$

Assertion(A): If length of a wire is halved, its Young's modulus of elasticity will become two times.

Reason(R): The ratio of longitudinal stress and longitudinal strain is called Young's modulus of elasticity.

Two wires of same material and length but radii in the ratio 2:3 are stretched by two forces to produce equal elongation. The ratio of two forces is

The upper end of a wire 1 m log and 2 mm radius is clamped. The lower end is twisted through angle of ${45^0}$. The angle of shear is

The length of an elastic string is a metre when the tension is 44 N, and b metre when the tension is 5 N. The length in metre when the tension is 9 N, is

The Young's modulus of a wire is $Y$, if the energy per unit volume is $E$, then the strain will be

An iron bar of length $L$, cross-section $A$ and Young’s modulus $Y$ is pulled by a force $F$ from both ends so as to produce an elongation $l$. Which of the following statement is correct?

Wires A and B are made from the same material. A has twice the diameter and three times the length of B. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in A to that in B is

An area of cross-section of rubber string is $2c{m^2}$. Its length is doubled when stretched with a linear force of $2 \times {10^5}dynes$. The Young’s modulus of the rubber in $dyne/c{m^2}$ will be

The Poisson’s ratio of a material is $0.1$. If the longitudinal strain of a rod of this material is ${10^{ - 3}}$, then the percentage change in the volume of the rod will be

Identify the incorrect statement.

Young’s modulus of the wire depends on

Young's modulus for rigid material is

Which is the most elastic

A cube of side 10 cm is subjected to a tangential force of $5 \times {10^5}\,\mathrm{N}$ at the upper face, keeping lower face fixed. The upper face is displaced by 0.001 radian relative to the lower face along the direction of tangential force. The shear modulus of the material of the cube is

A circular tube of mean radius $8 \mathrm{~cm}$ and thickness $0.04 \mathrm{~cm}$ is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is

Two wires of copper having the length in the ratio 4: 1 and their radii ratio as 1: 8 are stretched by the same force. The ratio of longitudinal strain in the two will be

The isothermal elasticity of a gas is equal to

What is the phenomenon of temporary delay in regaining the original configuration by an elastic body, after the removal of a deforming force?