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.	\(F/4\)

Steel and copper wires of the same length and area are stretched by the same weight one after the other. Young's modulus of steel and copper are \(2\times10^{11} ~\text{N/m}^2\) and  \(1.2\times10^{11}~\text{N/m}^2.\) The ratio of increase in length is: 

Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:

On applying stress of \(20 \times 10^{8}~\text{N/m}^2\), the length of a perfectly elastic wire is doubled. It's Young’s modulus will be:

The ratio of lengths of two rods \(A\) and \(B\) of the same material is \(1:2\) and the ratio of their radii is \(2:1\). The ratio of modulus of rigidity of \(A\) and \(B\) will be:

When a spiral spring is stretched by suspending a load on it, the strain produced is called:

A cube of aluminium of sides \(0.1~\text{m}\) is subjected to a shearing force of \(100\) N. The top face of the cube is displaced through \(0.02\) cm with respect to the bottom face. The shearing strain would be:
1. \(0.02\)                                   
2. \(0.1\)
3. \(0.005\)                               
4. \(0.002\)

The strain-stress curves of three wires of different materials are shown in the figure. \(P\), \(Q\) and \(R\) are the elastic limits of the wires. The figure shows that:
           

A \(5~\text{m}\) long wire is fixed to the ceiling. A weight of \(10~\text{kg}\) is hung at the lower end and is \(1~\text{m}\) above the floor. The wire was elongated by \(1~\text{mm}.\) The energy stored in the wire due to stretching is:
1. zero                        
2. \(0.05~\text J\) 
3. \(100~\text J\)                          
4. \(500~\text J\)