A gas undergoes a process in which its pressure P and volume V are related as ${\mathrm{VP}}^{\mathrm{n}}=\mathrm{constant}$. The bulk modulus for the gas in the process is 
 [Only for Dropper and XII batch]

1. $\frac{P}{n}$

2. $P^{1/n}$

3. nP

4. $P^n$

The Young's modulus of a wire of length 'L' and radius 'r' is 'Y'. If length is reduced to L/2 and radius r/2, then Young's modulus will be 

1. Y/2

2. Y

3. 2Y

4. 4Y

Three wires A,B,C made of the same material and radius have different lengths. The graphs in the figure show the elongation-load variation. The longest wire is 

1. A

2. B

3. C

4. All

The breaking stress of a wire depends upon

1. material of the wire

2. length of the wire

3. radius of the wire

4. shape of the cross section

The elastic energy stored in a wire of Young's Modulus Y is -

1. $\mathrm{Y}\times \frac{{\mathrm{strain}}^2}{\mathrm{volume}}$

2. $\mathrm{stress}\times \mathrm{strain}\times \mathrm{volume}$

3. $\frac{{\mathrm{strain}}^2\times \mathrm{volume}}{2\mathrm{Y}}$

4. $\frac{1}{2}\times stress\times strain\times volume$

If Young modulus (Y) equal to bulk modulus (B). Then the Poisson ratio is :

1. $\frac{1}{3}$

2. $\frac{2}{3}$

3. $\frac{1}{2}$

4. $\frac{1}{4}$

If a spring of spring constant k is stretched by a length x under tension T, the energy stored is 

1. $\frac{2k}{T^2}$

2. $\frac{2T^2}{k}$

3. $\frac{T^2}{2k}$

4. $\frac{2T}{k^2}$

A wire of length L and radius r is fixed at one end and a force F applied to the other end produces an extension l. The extension produced in another wire of the same material of length 2L and radius 2r by a force 2F is

1. l

2. 2l

3. l/2

4. 4l

The length of a spring is l₁ and l₂, when stretched with a force of 4 N and 5 N respectively. Its natural length is

1. l₂ + l₁

2. 2(l₂-l₁)

3. 5l₁ - 4l₂

4. 5l₂ - 4l₁

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

(a) Y                           (b) 4Y

(c) 8Y                            (d) $\frac{Y}{8}$