Mechanical properties of solids practice · Mixed difficulty

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

The maximum stress that can be applied to the material of a wire used to suspend an elevator is $1.3 \times 10^8 \mathrm{~Nm}^{-2}$. If the mass of the elevator is $900 \mathrm{~kg}$ and it moves up with an acceleration of $2.2 \mathrm{~ms}^{-2}$, what is the minimum diameter of the wire?

A cable is replaced by another one of the same length and material but of twice the diameter. The maximum load that the new wire can support without exceeding the elastic limit, as compared to the load that the original wire could support, is

If the ratio of lengths, radii and Young's moduli of steel and copper are 4, 3 and 2 respectively. The ratio of their increase in lengths would be (same force $F$ is applied to them)

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

If Poisson's ratio $\sigma$ for a material is $-\frac{1}{2}$, then the material is

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

Given below are two statements: one is labelled as
Assertion (A) and the other is labelled as Reason
(R).

Assertion (A): The property of body, by virtue of
which it tends to regain its original shape when the
external force is removed, is Elasticity.

Reason (R): The restoring force depends upon the
bonded inter atomic and inter molecular force of
solid.

In the light of the above statements, choose the
correct answer from the options given below:

The breaking stress for a wire of radius $\mathrm{r}$ of given material is $\mathrm{F} \mathrm{~N} / \mathrm{m}^2$. The breaking stress for the wire of same material of radius $2 \mathrm{r}$ is:

For steel $Y=2 \times 10^{11} \mathrm{Nm}^{-2}$. The force required to double the length of a steel wire of area $1 \mathrm{~cm}^2$ is

An elongation of 0.4% in a wire of cross-sectional area is ${10^{ - 6}}\,{m^2}$ causes a tension of 100 N. Y for the wire is $[\mathrm{in }\,\,N/{m^2}]$

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.

What is the formula for force when a rod fixed between two rigid support at both end. A temperature is changed by $\Delta {T}, {Y}$-young modulus, $\boldsymbol{\alpha}=$ coefficient of linear expension :

The length of a wire is 4 m. Its length is increased by 2 mm when a force acts on it. The strain is

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.

A steel wire of 6 mm diameter is stretched by applying a stress in the wire is $3 \times {10^6}\,N/{m^2}.$ Find the applied force in stretched wire

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.

A force of 200 N is applied at one end of a wire of length $2m$ and having area of cross-section ${10^{ - 2}}c{m^2}$. The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire $\alpha = 8 \times {10^{ - 6}}/{\,^0}C$ and Young’s modulus $Y = 2.2 \times {10^{11}}\;N/{m^2}$ and its temperature is increased by ${5^0}C$, then the increase in the tension of the wire will be

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