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 \(5\) 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. \(\frac{Kl}{2}\)
2. \(Kl\)
3. \(\frac{Kl^2}{2}\)
4. \(Kl^2\)

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:
\(Y = 9\times10^{11}~\text{N/m}^2\)
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. \(\frac{2}{\rho g}\)
2. \(\frac{\rho}{\sigma g}\)
3. \(\frac{\rho g}{2 \sigma}\)
4. \(\frac{\sigma}{\rho g}\)