Q. No.
Two blocks of masses \(2m\), \(m\) are placed on a smooth horizontal table and they are in contact on their smooth slanted surfaces. A horizontal force \(F\), equal to \(mg\), is applied to the system from the left, which causes them to accelerate. Let \(N_A\) be the normal reaction from the table on \(A\), and \(N_B\) on \(B\). Then,
1.
\(N_A = 2mg, N_B = mg\)
2.
\(N_A >2mg, N_B < mg\)
3.
\(N_A < 2mg, N_B > mg\)
4.
\(N_A < 2mg, N_B < mg\)
A block of mass \(M\) lies at rest on a horizontal table.
| Statement I: | (Newton's 3rd Law) To every action, there is an equal and opposite reaction. Action and reaction forces act on different bodies and in opposite directions. |
| Statement II: | The normal reaction is the reaction force, while the weight is the action. |
| 1. | Statement I is True, Statement II is True and Statement I is the correct reason for Statement II. |
| 2. | Statement I is True, Statement II is True and Statement I is not the correct reason for Statement II. |
| 3. | Statement I is True, Statement II is False. |
| 4. | Statement I is False, Statement II is True. |
Blocks \(A\) and \(B\) are connected as shown by an ideal string passing over a smooth pulley and released from rest. Take \(g = 10~\text{m/s}^2.\) The acceleration of the block \(B,\) relative to \(A,\) will be:
1. \(5~\text{m/s}^2\)
2. \(4~\text{m/s}^2\)
3. \(2~\text{m/s}^2\)
4. \(1~\text{m/s}^2\)
The two blocks are at rest on a smooth horizontal plane and are connected by strings passing over a smooth light pulley as shown. The strings are vertical while the force \(F,\) applied to the pulley is vertical. For what minimum value of \(F\) will the \(2\) kg block be lifted off?
(\(g=10\) m/s2)
| 1. | \(20\) N | 2. | \(30\) N |
| 3. | \(25\) N | 4. | \(40\) N |
An astronaut, in a space shuttle, orbiting close to the earth's surface (take \(g= 10~\text{m/s}^2\)), suddenly fires his engines so as to give him a forward acceleration of \(\dfrac{3g}{4}\) along the direction of his motion. At that instant, his apparent weight is:
| 1. | \(25\%\) more than his real weight. |
| 2. | \(25\%\) less than his real weight. |
| 3. | \(75\%\) more than his real weight. |
| 4. | \(75\%\) less than his real weight. |
The mass \(m\) can slide along a smooth radial groove in a horizontal turntable; at the other end is attached a spring- so that the mass \(m\) presses against the spring as it moves 'outward'. The free-end (\(A\)) of the spring is at a distance \(b\) from the centre and the spring constant is \(k.\) If the turntable is rotated with an angular speed \(\omega\), and the mass \(m\) is in 'equilibrium' with the spring compressed, then the compression is:
| 1. | \(\dfrac{m\omega^2b}{k}\) |
| 2. | \(\dfrac{m\omega^2b}{k-m\omega^2}\) |
| 3. | \(\dfrac{m\omega^2b}{m\omega^2-k}\) |
| 4. | \(\dfrac{m\omega^2b}{m\omega^2+k}\) |
1. \(1000~\text{N}\)
2. \(2500~\text{N}\)
3. \(1500~\text{N}\)
4. \(3500~\text{N}\)
A ball of mass \(m\) falls from a height \(h\) onto the ground and rebounds to a height \(\dfrac{h}{4}\). The impulse on the ball from the ground has the magnitude:
| 1. | \(\dfrac{3}{4}m\sqrt{2gh}\) |
| 2. | \(\dfrac{5}{4}m\sqrt{2gh}\) |
| 3. | \(\dfrac{3}{2}m\sqrt{2gh}\) |
| 4. | \(\dfrac{1}{2}m\sqrt{2gh}\) |
A block of mass \(m,\) placed on a rough incline (as shown) – is observed to remain at rest. The coefficient of friction is \(\mu.\) The net force exerted by the incline on the block equals: (in magnitude)
1. \(mg \cos\theta +\mu mg\cos\theta\)
2. \(mg\cos\theta\sqrt{1+\mu^2}\)
3. \(mg\sin\theta\)
4. \(mg\)
| 1. | as \(\dfrac{m_1 }{m_2} \rightarrow 1 , a \rightarrow 0\) |
| 2. | as \(\dfrac{m_1 }{m_2} \rightarrow 0 , a \rightarrow g\) |
| 3. | \(a\) varies linearly with \(\dfrac{m_1 }{m_2}\) |
| 4. | all the above are true. |
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