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