In the CGS system, Young's modulus of a steel wire is 2×10¹² dyne/cm². To double the length of a wire of unit cross-section area, the force required is:
1. 4×10⁶ dynes
2. 2×10¹² dynes
3. 2×10¹² newtons
4. 2×10⁸ 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:
1. 1: 16                                             
2. 16: 1
3. 1: 64                                             
4. 64: 1

The work done in stretching an elastic wire per unit volume is:

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

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

The work done per unit volume to stretch the length of a wire by 1%  with a constant cross-sectional area will be: $\left[Y=9\times {10}^{11}N/m^2\right]$

1. $9\times {10}^{11}$ $J$

2. $4.5\times {10}^{7}J$

3. $9\times {10}^{7}J$

4. $4.5\times {10}^{11}$ $J$

lf $\mathrm{\rho }$ 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.$\frac{2}{\mathrm{\rho g}}$

2. $\frac{\mathrm{\rho }}{\mathrm{\sigma g}}$

3.$\frac{\mathrm{\rho g}}{2\mathrm{\sigma }}$

4. $\frac{\mathrm{\sigma }}{\mathrm{\rho g}}$

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%