A uniform wire of cross-sectional area A is stretched by a certain force so that its length is elongated by x. What should be the cross-sectional area of the wire, so that elongation becomes $\frac{\mathrm{x}}{2}$ on applying the same force?

(1) A

(2) 2A

(3) 4A

(4) 8A

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

(1) Incompressible

(2) Elastic fatigue

(3) Compressible

(4) Plastic

The curve between potential energy \((U)\) and distance \((r)\) between atoms of a diatomic molecule is shown in the figure. If \(\vec F_A, \vec F_B,\vec F_C,\vec {F_D},\) and \(\vec F_{E}\) are forces of interaction between atoms of molecule corresponding to points shown on the curve, then:

1.  \(\left|\vec F _{A}\right|   <   \left|\vec F _{B}\right| <   \left|\vec F _{D}\right| \)

2.  \(\left|\vec F _{B}\right|   =   0\)

3.  \(\left|\vec F _{C}\right| . \left|\vec F _{E}\right|<   0\)

4.  \(\left|\vec F _{D}\right| . \left|\vec F _{C}\right|   >   0\)$\mathrm{}$

The adiabatic elasticity of helium gas at STP will be:
1. \( 1.13 \times 10^5 ~\text{Pa}\)
2. \( 1.25 \times 10^5 ~\text{Pa}\)
3. \( 1.33 \times 10^5 ~\text{Pa}\)
4. \(1.67 \times 10^5 ~\text{Pa}\)

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: