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:
                    
1. \(A\)
2. \(B\)
3. \(C\)
4. All of the above

The breaking stress of a wire depends upon:

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. \(\frac{3P}{B}\)
4. \(\frac{P}{3B}\)

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 

When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, then the increase in length will be -

1. 0.5 cm                             

2. 2 cm

3. 4 cm                                 

4. 8 cm

The material which practically does not show elastic after effect is 

1. Copper                         

2. Rubber

3. Steel                             

4. Quartz

A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be: