The area of cross-section of a wire of length \(1.1\) m is \(1\) mm2. It is loaded with mass of \(1\) kg. If Young's modulus of copper is \(1.1\times10^{11}\) N/m2, then the increase in length will be: (If \(g = 10~\text{m/s}^2)\)
1. | \(0.01\) mm | 2. | \(0.075\) mm |
3. | \(0.1\) mm | 4. | \(0.15\) mm |
In the CGS system, Young's modulus of a steel wire is \(2\times 10^{12}\) dyne/cm2. To double the length of a wire of unit cross-section area, the force required is:
1. \(4\times 10^{6}\) dynes
2. \(2\times 10^{12}\) dynes
3. \(2\times 10^{12}\) newtons
4. \(2\times 10^{8}\) dynes
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. | \(64:1\) |
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
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.
2.
3.
4.
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. \(\frac{\sigma}{\rho g}\)