A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\dfrac{T_1+T_2}{2}\). Then,
1. | \(A=\dfrac{A_1+A_2}{2},~l=\dfrac{l_1+l_2}{2}\) |
2. | \(l=\dfrac{l_1+l_2}{2}\) |
3. | \(A=\dfrac{A_1+A_2}{2}\) |
4. | \(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
1. | tensile, \(F \over 3A\) |
2. | compressive, \(F \over 3A\) |
3. | tensile, \(2F \over 3A\) |
4. | compressive, \(2F \over 3A\) |
When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.
1. | this energy completely appears as the increased kinetic energy of the block |
2. | this energy completely appears as the increased elastic potential energy of the wire |
3. | this energy completely appears as heat |
4. | none of these |
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:
1. | when the mass is at the highest point |
2. | when the mass is at the lowest point |
3. | when the wire is horizontal |
4. | at an angle of \(\cos^{-1}(\frac{1}{3})\) from the upward vertical |
The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:
1. \(\frac{l_{1}+l_{2}}{2}\)
2. \(\sqrt{l_{1} l_{2}}\)
3. \(\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)
4. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)
A rope \(1\) cm in diameter breaks if the tension in it exceeds \(500\) N. The maximum tension that may be given to a similar rope of diameter \(2\) cm is:
1. \(500\) N
2. \(250\) N
3. \(1000\) N
4. \(2000\) N
1. | 2. |
3. | 4. |
1. | (stress)2 × strain | 2. | stress × strain |
3. | \(\dfrac12\) × stress × strain | 4. | stress × (strain)2 |
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. |