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

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. $\frac{\mathrm{3P}}{B}$

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:

1. 1:2

2. 2:1

3. 4:1

4. 1:1

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:
1. \(F/2\)                                     
2. \(2F\) 
3. \(4F\)
4. \(F/4\)