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:

[This question includes concepts from Kinetic Theory chapter]

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
    

The breaking stress of a wire depends upon:

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. $\frac{1}{4}$

A constrained steel rod of length l, area of cross-section A, Young's modulus Y and coefficient of linear expansion $\alpha$ is heated through \(t^{\circ}\mathrm{C}\)$$. The work that can be performed by the rod when heated is:
1. (YA$\alpha$t)(l$\alpha$t)
2. $\frac{1}{2}$(YA$\alpha$t)(l$\alpha$t)
3. $\frac{1}{2}$(YA$\alpha$t)$\frac{1}{2}$(l$\alpha$t)
4. 2(YA$\alpha$t)(l$\alpha$t)

The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius will be:

1. $\frac{P}{B}$

2. $\frac{B}{3P}$

3. $\frac{\mathrm{3P}}{B}$

4. $\frac{P}{3B}$

The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of:

Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is  Δl. Which of the following graphs is a straight line?

(1) Δl versues 1/l

(2) Δl versus l²

(3) Δl versus 1/l²

(4) Δl versus l

The following four wires are made of the same material. Which of them will have the largest extension when the same tension is applied?

(1) Length=50 cm, diameter=0.5 mm 

(2) Length=100 cm, diameter=1 mm 

(3) Length=200 cm, diameter=2 mm 

(4) Length=300 cm, diameter=3 mm