A force applied on a brass wire of uniform cross-section area creates change in its length and cross-sectional area. If lateral strain produced in the wire is $3<mspace\; width="1em"></mspace>\mathrm{x}<mspace\; width="1em"></mspace>{10}^{-2}$, then the energy stored per unit volume of wire will be: [${\mathrm{Y}}_{\mathrm{brass}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>9<mspace\; width="1em"></mspace>\mathrm{x}<mspace\; width="1em"></mspace>{10}^{10}<mspace\; width="1em"></mspace>\mathrm{N}/{\mathrm{m}}^2,<mspace\; width="1em"></mspace>{\mathrm{\sigma }}_{\mathrm{brass}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>0.3$]

(1) 275 $\mathrm{MJ}/{\mathrm{m}}^3$

(2) 315 $\mathrm{MJ}/{\mathrm{m}}^3$

(3) 450 $\mathrm{MJ}/{\mathrm{m}}^3$

(4) 175 $\mathrm{GJ}/{\mathrm{m}}^3$

A steel ring of radius r and cross-section area A is fitted on to a wooden disc of radius R (R > r). If Y is Young's modulus of elasticity, then tension with which the steel ring is expanded is:

1.  $\frac{\mathrm{AYR}}{\mathrm{r}}$

2.  $\frac{\mathrm{AY}\left(\mathrm{R}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{r}\right)}{\mathrm{r}}$

3.  $\frac{\mathrm{Y}\left(\mathrm{R}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{r}\right)}{\mathrm{Ar}}$

4.  $\frac{\mathrm{Yr}}{\mathrm{AR}}$

Given that the breaking stress of a wire is 7.2 x ${10}^7$ N/ ${\mathrm{m}}^2$ and its density is 7.2 g/cc, then the maximum length of the wire which can hang without breaking is: (g = 10 m/${\mathrm{s}}^2$)

(1) 1000 m

(2) 100 m

(3) 200 m

(4) 50 m

If the pressure of a gas is increased from 1.04 x ${10}^5$ Pa to 1.045 x ${10}^5$ Pa and volume is decreased by 5% at a constant temperature, then the Bulk modulus of the gas is:

(1) 1.0425 x ${10}^5$ Pa

(2) 1.045 x ${10}^5$ Pa

(3) ${10}^4$ Pa

(4) 2.5 x ${10}^4$ Pa

The stress-strain curve for two materials \(A\) and \(B\) are as shown in the figure. Select the correct statement:

Select the incorrect statement about Bulk modulus of elasticity.

(1) It is defined for solids, liquids and gases.

(2) ${\mathrm{B}}_{\mathrm{solid}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{B}}_{\mathrm{liquid}}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{B}}_{\mathrm{gas}}$

(3) The bulk modulus of gas is different for different processes.

(4) Almost for all materials, the Bulk modulus increases with the rise in temperature.

The figure below shows the stress-strain curve for two bodies A and B.

Choose the correct option.

(1) A is having greater elasticity than B.

(2) B is having a greater elasticity than A.

(3) Both A and B have the same elasticity.

(4) A and B both show plasticity.

When a load of 1 kg is hung from the wire, then the extension of 2 mm is produced. Then work done by restoring force is:

(1) 200 mJ

(2) 400 mJ

(3) 10 mJ

(4) 20 mJ

Stress vs strain graphs for two different wires \(A\) and \(B\) are given. If \(Y_A\) and \(Y_B\) are Young's moduli of the materials, then:
                  
1. \(Y_{A}=\sqrt{3} Y_{B} \)
2. \( \sqrt{3} Y_{A}=Y_{B} \)
3. \(Y_{A}=3 Y_{B} \)
4. \( 3 Y_{A}=Y_{B} \)