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%

If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are \(a,\) \(b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths will be:

1. $\frac{2a^{2}c}{b}$

2. $\frac{3a}{2b^{2}c}$

3. $\frac{2ac}{b^2}$

4. $\frac{3c}{2a{b}^2}$

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. $4.5\times {10}^{11}$ $J$

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 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 \(5\) 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 work done in stretching an elastic wire per unit volume 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

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: