On applying stress of \(20 \times 10^{8}~\text{N/m}^2\), the length of a perfectly elastic wire is doubled. It's Young’s modulus will be:
1. | \(40 \times 10^{8}~\text{N/m}^2\) | 2. | \(20 \times 10^{8}~\text{N/m}^2\) |
3. | \(10 \times 10^{8}~\text{N/m}^2\) | 4. | \(5 \times 10^{8}~\text{N/m}^2\) |
The ratio of lengths of two rods \(A\) and \(B\) of the same material is \(1:2\) and the ratio of their radii is \(2:1\). The ratio of modulus of rigidity of \(A\) and \(B\) will be:
1. | \(4:1\) | 2. | \(16:1\) |
3. | \(8:1\) | 4. | \(1:1\) |
When a spiral spring is stretched by suspending a load on it, the strain produced is called:
1. | Shearing |
2. | Longitudinal |
3. | Volume |
4. | shearing and longitudinal |
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:
1. | Elasticity of wire \(P\) is maximum. |
2. | Elasticity of wire \(Q\) is maximum. |
3. | Tensile strength of \(R\) is maximum. |
4. | None of the above is true. |
1. | \(\times\)strain | stress
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. \(\frac{Kl}{2}\)
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. \(\frac{E}{Y}\)