Q. No.A particle of mass \(m\) is attached to a string and is moving in a vertical circle. Tension in the string when the particle is at its highest and lowest point is \(T_1\) \(T_2\) respectively. Here \(T_2-T_1\) is equal to:
| 1. | \(mg\) | 2. | \(2mg\) |
| 3. | \(4mg\) | 4. | \(6mg\) |
1. \(\frac{3}{2}D\)
2. \(D\)
3. \(\frac{7}{4}D\)
4. \(\frac{5}{4}D\)
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine?
| 1. | 12.3 kW | 2. | 7.0 kW |
| 3. | 10.2 kW | 4. | 8.1 kW |
| 1. | \(W_1=W_2=W_3\) | 2. | \(W_1>W_2>W_3\) |
| 3. | \(W_1>W_3>W_2\) | 4. | \(W_1<W_2<W_3\) |
| 1. | no work is done by the tangential force. |
| 2. | no work is done by the centripetal force. |
| 3. | work done by the tangential force is always positive. |
| 4. | work done by the centripetal force is negative. |
Consider a drop of rainwater having a mass of \(1~\text{gm}\) falling from a height of \(1~\text{km}.\) It hits the ground with a speed of \(50~\text{m/s}.\) Take \(g\) as constant with a value \(10~\text{m/s}^2.\) The work done by the
(i) gravitational force and the (ii) resistive force of air is:
| 1. | \((\text{i})~1.25~\text{J};\) \((\text{ii})~-8.25~\text{J}\) |
| 2. | \((\text{i})~100~\text{J};\) \((\text{ii})~8.75~\text{J}\) |
| 3. | \((\text{i})~10~\text{J};\) \((\text{ii})~-8.75~\text{J}\) |
| 4. | \((\text{i})~-10~\text{J};\) \((\text{ii})~-8.75~\text{J}\) |
A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
| 1. | inclined at an angle of \(60^{\circ}\) from vertical. |
| 2. | the mass is at the highest point. |
| 3. | the wire is horizontal. |
| 4. | the mass is at the lowest point. |
| 1. | \(\left(2 t^2+4 t^4\right)~\text W\) | 2. | \(\left(2 t^3+3 t^3\right) ~\text W\) |
| 3. | \(\left(2 t^3+3 t^5\right) ~\text W\) | 4. | \(\left(2 t^3+3 t^4\right) ~\text W\) |
A stone is dropped from a height \(h.\) It hits the ground with a certain momentum \(p.\) If the same stone is dropped from a height \(100\%\) more than the previous height, the momentum when it hits the ground will change by:
1. \(41\%\)
2. \(200\%\)
3. \(100\%\)
4. \(68\%\)
A moving block having mass \(m\) collides with another stationary block having a mass of \(4m.\) The lighter block comes to rest after the collision. When the initial velocity of the lighter block is \(v,\) then the value of the coefficient of restitution \((e)\) will be:
1. \(0.5\)
2. \(0.25\)
3. \(0.8\)
4. \(0.4\)
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