Q. No.| 1. | zero | 2. | \(\frac{2W}{A}\) |
| 3. | \(\frac{W}{A}\) | 4. | \(\frac{W}{2A}\) |
The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):
| 1. | ductile and brittle |
| 2. | brittle and ductile |
| 3. | brittle and plastic |
| 4. | plastic and ductile |
1. \(0.4~\text{mm}\)
2. \(40~\text{mm}\)
3. \(8~\text{mm}\)
4. \(4~\text{mm}\)
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. | \(\dfrac{{MgL}_1}{{AL}}\) |
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. | \(F\) |
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. | \(\dfrac{5 q}{\left(7 {sp}^2\right)} \) | 2. | \(\dfrac{7 q}{\left(5 sp^2\right)} \) |
| 3. | \(\dfrac{2 q}{(5 s p)} \) | 4. | \(\dfrac{7 q}{(5 s p)}\) |
| Assertion (A): | The stretching of a spring is determined by the shear modulus of the material of the spring. |
| Reason (R): | A coil spring of copper has more tensile strength than a steel spring of the same dimensions. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is False but (R) is True. |
| 4. | (A) is True but (R) is False. |
The bulk modulus of a spherical object is \(B.\) If it is subjected to uniform pressure \(P,\) the fractional decrease in radius is:
| 1. | \(\frac{B}{3P}\) | 2. | \(\frac{3P}{B}\) |
| 3. | \(\frac{P}{3B}\) | 4. | \(\frac{P}{B}\) |
(given: Young's modulus of the wire = \(Y=2.0\times 10^{11}~\text{N/m}^2\))
1. \(10^{11}~\text{J/m}^3\)
2. \(10^{17}~\text{J/m}^3\)
3. \(10^{7}~\text{J/m}^3\)
4. \(10^{5}~\text{J/m}^3\)
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