Mechanical properties of solids practice · Medium

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

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

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?

The elastic energy stored in a wire of Young’s modulus $Y$ is

A wire of Young’s modulus $1.5 \times {10^{12}}\;\mathrm{N}{\mathrm{m}^{ - 2}}$ is stretched by a force so as to produce a strain of $2 \times {10^4}.$ The energy stored per unit volume is

Two wires of the same material and same mass are stretched by the same force. Their lengths are in the ratio 2 : 3. Then their elongations are in the ratio

The expression of force constant for a spring following Hooke's law is given by:

Longitudinal stress of $1N/m{m^2}$ is applied on a wire. The percentage increase in length is $\left( {Y = {{10}^{11}}N/{m^2}} \right)$

The Young’s modulus of a wire of length $L$ and radius $r$ is $Y\mathrm{ }N/{m^2}$. If the length and radius are reduced to $L/2$ and $r/2$, then its Young’s modulus will be

The increases in length is $l$ of a wire of length $L$ by the longitudinal stress. Then the stress is proportional to

The bulk modulus of an ideal gas at constant temperature

A cube is shifted to a depth of 100 m in a lake. The change in volume is $0.1\%$. The bulk modulus of the material is nearly

A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire

Statement I: Lead is more elastic than rubber.
Statement II: If the same load is attached to lead and rubber wires of the same cross-sectional area, the strain of lead is very much less than that of rubber.

Statement-I: Spring balances show correct readings even after they had been used for a long time.
Statement-II: On using for long time, spring balances losses its elastic strength.

The value of Poisson’s ratio lies between

If Young’s modulus of elasticity $Y$ for a material is one and half times its rigidity coefficient $\eta$, the Poisson’s ratio $\sigma$ will be

Statement I: Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.
Statement II: Steel is more elastic than copper.

For a constant hydraulic stress on an object, the fractional change in the object’s volume $\left( {\frac{{\Delta V}}{V}} \right)$ and its bulk modulus ($B$) are related as

Statement I: Stress is the internal force per unit area of the body.
Statement II: Rubber is more elastic than steel.