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.  $\frac{\mathrm{AY}\left(\mathrm{R} - \mathrm{r}\right)}{\mathrm{r}}$

3.  $\frac{\mathrm{Y}\left(\mathrm{R} - \mathrm{r}\right)}{\mathrm{Ar}}$

4.  $\frac{\mathrm{Yr}}{\mathrm{AR}}$

Young's modulus of a material is 2.4 times that of its modulus of rigidity. Its Poisson's ratio is:

(1) 1. 2

(2) 2. 4

(3) 0. 2

(4) 0. 4

The longitudinal strain of a string is equal to twice the magnitude of lateral strain. Poisson's ratio of the material of string is:

(1) 0.4

(2) 0.5

(3) 0.1

(4) 0.2

When a mass M is suspended by a wire, it elongates the wire by length l. The work done during this elongation process is:

(1) Zero

(2) $\frac{1}{2}$Mgl

(3) Mgl

(4) 2Mgl

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

Work done in increasing the length of a 1 m long wire by 1 mm is 10 J. Work done in increasing the length further by 1 mm is:

(1) 10 J

(2) 20 J

(3) 30 J

(4) 40 J

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 breaking strength of the iron wire of radius r and length l is 2 x ${10}^6 \mathrm{N}/{\mathrm{m}}^2$. Breaking strength of another iron wire of radius r, and length l at the same temperature will be:

(1) 0.5 x ${10}^6 \mathrm{N}/{\mathrm{m}}^2$

(2) 1 x ${10}^6 \mathrm{N}/{\mathrm{m}}^2$

(3) 2 x ${10}^6 \mathrm{N}/{\mathrm{m}}^2$

(4) 8 x ${10}^6 \mathrm{N}/{\mathrm{m}}^2$

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

A material has Poisson's ratio of 0.5 and  If a uniform rod of it suffers a longitudinal strain of 4 x ${10}^{-6}$, then the percentage change in its volume will be

(1) 2%

(2) 8%

(3) 0%

(4) 4%