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:

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:

The relationship between Young's modulus Y, Bulk modulus K and modulus of rigidity n is

(1) $Y=\frac{9nK}{n+3K}$                                    

(2) $\frac{9YK}{Y+3K}$ 

(3)  $Y=\frac{9nK}{3+K}$                                     

(4) $Y=\frac{3nK}{9n+K}$         

The Young's modulus of a rubber string 8 cm long and density $1.5 kg/m^3$ is $5\times {10}^8 N/m^2$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

(1) $9.6\times {10}^{-5} m$                           

(2) $9.6\times {10}^{-11}m$

(3) $9.6\times {10}^{-3} m$                           

(4) 9.6 m

A and B are two wires of same material. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is

(1) Equal to that on A

(2) Four times that on A

(3) Two times that on A               

(4) Half that on A