Mechanical properties of solids practice · Mixed difficulty

If $x$ longitudinal strain is produced in a wire of Young’s modulus $y$, then energy stored in the material of the wire per unit volume is

Statement I: Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Both the balls will rise to same height after bouncing.
Statement II: Ivory and wet-clay have same elasticity.

Thermal stress, If developed in a solid on heating is given by

On all the six surfaces of a unit cube, equal tensile force of $F$ is applied. The increase in length of each side will be $(Y =$ Young’s modulus, $\sigma =$ Poisson’s ratio)

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

Rubber is an example of

A tensile force of $2 \times {10^3}\,\mathrm{N}$ doubles the length of a rubber band of cross-sectional area $2 \times {10^{ - 4}}\,{\mathrm{m}^2}$. The Young’s modulus of elasticity of the rubber band is

A steel wire of length 2 m and Young's modulus $2.0 \times 10^{11} \mathrm{Nm}^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is _____ $\times 10^5$ (in SI units)

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

The general form of potential energy curve for atoms or molecules can be represented by the following equation $U\left( R \right) = \frac{A}{{{R^n}}} - \frac{B}{{{R^m}}}$ . Here, R is the interatomic or molecular distance, A and B are coefficients, $n$ and $m$ are the exponents. In the above equation

A metal wire of length $L,$ area of cross section $A$ and Young's modulus $Y$ behaves as a spring of spring constant $k$ given by:

Which of the following statements is correct

The value of modulus of rigidity for ideal liquid is

If compressibility of a material is $4 \times 10^{-5}$ per atm, pressure is $100 \mathrm{~atm}$ and volume is $100 \mathrm{~cm}^3$, then find the value of $\Delta V$.

A long piece of rubber is wider than it is thick. When is is stretched in length by some amount:

A force $F$ is required to break a wire of length $I$ and radius $r$. What force is required to break a wire, of the same material, having twice the length and six times the radius ?

A metal wire of length $L$ is suspended vertically from a rigid support. When a body of mass $M$ is attached to the lower end of wire, the elongation of the wire is $\ell$, then the incorrect statement is

Young’s modulus of perfectly rigid body material is

A: To minimize the depression in a beam, it is designed as '${I}$' shape girder.
R: The '$I$' shape girders have large load bearing surface, which decreases the stress

The specific heat at constant pressure and at constant volume for an ideal gas are ${C_p}$ and ${C_v}$ and its adiabatic and isothermal elasticities are ${E_\phi }$ and ${E_\theta }$ respectively. The ratio of ${E_\phi }$ to ${E_\theta }$ is

The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$. If $B$ is the bulk modulus of the metal, then the ratio $\rho^{\prime} / \rho$ is

Which of the following statements is/are wrong?
I. Hollow shaft is much stronger than a solid rod of same length and same mass
II. Reciprocal of bulk modulus of elasticity is called compressibility
III. It is difficult to twist a long rod as compared to small rod.

Which one of the following statements is correct? In the case of

On stretching a wire, the elastic energy stored per unit volume is

A load suspended by a massless spring produces an extension of $x\,\,cm$ in equilibrium. When it is cut into two unequal parts, the same load produces an extension of $7.5\,\,cm$ when suspended by the larger part of length 60 cm. When it is suspended by the smaller part, the extension is 5.0 cm Then

Given below are two statements : One is labelled as, Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements, choose the most, appropriate answer from the options given below

A rigid bar of mass $M$ is supported symmetrically by three wires each of length $L$. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to

According to Hooke’s law of elasticity, if stress is increased, them the ratio of stress to strain

If the length of a wire is made double and radius is
halved of its respective values. Then, the Young's
modulus of the material of the wire will :

Assertion: If length of a rod is doubled, the breaking load remains the same.
Reason: Breaking load is equal to the elastic limit.