A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:
1. | \(F/2\) | 2. | \(2F\) |
3. | \(4F\) | 4. | \(F/4\) |
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:
1. | \(2 \over 5\) | 2. | \(3 \over 5\) |
3. | \(5 \over 4\) | 4. | \(5 \over 2\) |
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. | \(64:1\) |
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