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

1.	stress\(\times\)strain
2.	\(\frac{1}{2}\) \(\times\) stress\(\times\)strain
3.	\(2\times\) stress\(\times\)strain
4.	stress/strain

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

If the force constant of a wire is K, the work done in increasing the length of the wire by l is:

1. $Kl/2$                                   

2. $Kl$

3. $K{l}^2/2$                                 

4. $K{l}^2$

When strain is produced in a body within elastic limit, its internal energy:
1. Remains constant                  
2. Decreases
3. Increases                               
4. None of the above

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

An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is:

1. $\frac{SY}{2}$ $$ $$

2. $\frac{S^2}{2Y}$

3. $\frac{S}{2Y}$ $$

4. $\frac{2S}{Y}$

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%