In the CGS system, Young's modulus of a steel wire is \(2\times 10^{12}~\text{dyne/cm}^2.\) To double the length of a wire of unit cross-section area, the force required is:
1. \(4\times 10^{6}~\text{dynes}\)
2. \(2\times 10^{12}~\text{dynes}\)
3. \(2\times 10^{12}~\text{newtons}\)
4. \(2\times 10^{8}~\text{dynes}\)

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:

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. \(500~\text J\)

The Young's modulus of a wire is \(Y.\) If the energy per unit volume is \(E,\) then the strain will be:
1. \(\sqrt{\frac{2E}{Y}}\)
2. \(\sqrt{2EY}\)
3. \(EY\)
4. \(\frac{E}{Y}\)

A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:

1. \(\dfrac{Y x A}{2 L}\)

2. \(\dfrac{Y x^{2} A}{L}\)

3. \(\dfrac{Y x^{2} A}{2 L}\)

4. \(\dfrac{2 Y x^{2} A}{L}\)

The work done per unit volume to stretch the length of a wire by \(1\%\) with a constant cross-sectional area will be:
\((Y = 9\times10^{11}~\text{N/m}^2)\)
1. \(9\times 10^{11}~\text{J}\)
2. \(4.5\times 10^{7}~\text{J}\)
3. \(9\times 10^{7}~\text{J}\)
4. \(4.5\times 10^{11}~\text{J}\)

lf \(\rho\) is the density of the material of a wire and \(\sigma\) is the breaking stress, the greatest length of the wire that can hang freely without breaking is:
1. \(\dfrac{2}{\rho g}\)

2. \(\dfrac{\rho}{\sigma g}\)

3. \(\dfrac{\rho g}{2 \sigma}\)

4. \(\dfrac{\sigma}{\rho g}\)

A material has Poisson's ratio of \(0.5\). If a uniform rod made of it suffers a longitudinal strain of \(2\times 10^{-3}\), what is the percentage increase in volume?
1. \(2\%\)
2. \(4\%\)
3. \(0\%\)
4. \(5\%\)