Q. No.Two masses \(8~\text{kg}\) and \(12~\text{kg}\) are connected at the two ends of a light inextensible string that goes over a frictionless pulley. The acceleration of the masses and the tension in the string when the masses are released are:
1. \(2~\text{ms}^{-2}, 69~\text{N}\)
2. \(1~\text{ms}^{-2}, 69~\text{N}\)
3. \(2~\text{ms}^{-2}, 96~\text{N}\)
4. \(1~\text{ms}^{-2}, 96~\text{N}\)
A block \(A\) of mass \(7\) kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body \(B\) of mass \(3\) kg at the other end. The acceleration of the system will be: (given \(g=10~\text{m/s}^2)\)
| 1. | \(100\) ms–2 | 2. | \(3\) ms–2 |
| 3. | \(10\) ms–2 | 4. | \(30\) ms–2 |
Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:
| 1. | \(\dfrac{g}{2}\) | 2. | \(\dfrac{g}{5}\) |
| 3. | \(\dfrac{g}{10}\) | 4. | \(g\) |
The tension in the string connecting blocks, \(B\) and \(C\), placed on a smooth horizontal surface in the following diagram is:
| 1. | \(25\) N | 2. | \(30\) N |
| 3. | \(32.5\) N | 4. | \(37.5\) N |
A monkey weighing \(20\) kg is holding a vertical rope. The rope will not break when a mass of \(25\) kg is suspended from it but will break if the mass exceeds \(25\) kg. What is the maximum acceleration with which the monkey can climb up the rope? (\(g = 10\) m/s2)
1. \(5\) m/s2
2. \(10\) m/s2
3. \(25\) m/s2
4. \(2.5\) m/s2
If a young man of mass \(60\) kg stands on the floor of a lift which is accelerating downwards at \(1~\text{m/s}^2\), then the reaction of the floor of the lift on the man will be: \(\left(g = 9.8~\text{m/s}^2 \right)\)
| 1. | \(528\) N | 2. | \(540\) N |
| 3. | \(546\) N | 4. | None of these |
A small ball is suspended from a thread. If it is lifted up with an acceleration of \(4.9\) ms–2 and lowered with an acceleration of \(4.9\) ms–2, then the ratio of the tension in the thread in both cases will be:
1. \(1:3\)
2. \(3:1\)
3. \(1:1\)
4. \(1:5\)
A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:
| 1. | moving with constant velocity. |
| 2. | in accelerated motion. |
| 3. | in retarded motion. |
| 4. | at rest. |
The strings and pulleys shown in the figure are massless. The reading shown by the light spring balance \(S\) is:
| 1. | \(2.4\) kg | 2. | \(5\) kg |
| 3. | \(2.5\) kg | 4. | \(3\) kg |
Two masses, \(M\) and \(m\), are connected by a weightless string. They are pulled by a force on a frictionless horizontal surface. The tension in the string will be:
1. \(\frac{F \left(M + 2 m\right)}{m + M}\)
2. \(F \over {m +M}\)
3. \(\frac{FM}{m}\)
4. \(Fm \over {m + M}\)
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