Q. No.
| 1. | \(\dfrac{5 q}{\left(7 {sp}^2\right)} \) | 2. | \(\dfrac{7 q}{\left(5 sp^2\right)} \) |
| 3. | \(\dfrac{2 q}{(5 s p)} \) | 4. | \(\dfrac{7 q}{(5 s p)}\) |
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. | \(5 \over 2\) |
A metallic rope of diameter \(1~ \text{mm}\) breaks at \(10 ~\text{N}\) force. If the wire of the same material has a diameter of \(2~\text{mm},\) then the breaking force is:
| 1. | \(2.5~\text{N}\) | 2. | \(5~\text{N}\) |
| 3. | \(20~\text{N}\) | 4. | \(40~\text{N}\) |
The Young's modulus of a wire is numerically equal to the stress at a point when:
| 1. | The strain produced in the wire is equal to unity. |
| 2. | The length of the wire gets doubled. |
| 3. | The length increases by \(100\%.\) |
| 4. | All of these. |
In the CGS system, Young's modulus of a steel wire is \(2\times 10^{12}~\text{dyne/cm}^2.\) To double the length of a wire of unit cross-section area, the force required is:
1. \(4\times 10^{6}~\text{dynes}\)
2. \(2\times 10^{12}~\text{dynes}\)
3. \(2\times 10^{12}~\text{newtons}\)
4. \(2\times 10^{8}~\text{dynes}\)
Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area \(A\) and the second wire has a cross-sectional area \(3A\). If the length of the first wire is increased by \(\Delta l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount?
| 1. | \(9F\) | 2. | \(6F\) |
| 3. | \(4F\) | 4. | \(F\) |
A wire of length \(L,\) area of cross section \(A\) is hanging from a fixed support. The length of the wire changes to \({L}_1\) when mass \(M\) is suspended from its free end. The expression for Young's modulus is:
| 1. | \(\dfrac{{Mg(L}_1-{L)}}{{AL}}\) | 2. | \(\dfrac{{MgL}}{{AL}_1}\) |
| 3. | \(\dfrac{{MgL}}{{A(L}_1-{L})}\) | 4. | \(\dfrac{{MgL}_1}{{AL}}\) |
1. \(\Delta l ~\text{vs}~\dfrac{1}{l}\)
2. \(\Delta l ~\text{vs}~l^2\)
3. \(\Delta l ~\text{vs}~\dfrac{1}{l^2}\)
4. \(\Delta l ~\text{vs}~l\)
1. \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}} \)
2. \(\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2} \)
3. \(2 \mathrm{~L}_{1}-\mathrm{L}_{2} \)
4. \(3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}\)
A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively,
| (a) | weight hung and length increased |
| (b) | stress applied and length increased |
| (c) | stress applied and strain developed |
| (d) | length increased and the weight hung |
Choose the correct option:
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (a), (b) and (d) |
| 4. | all of these |
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