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Q. No.A flywheel with a moment of inertia of \(2~\text{kg-m}^2\) is initially rotating at an angular speed of \(30~\text{rad/s}.\) A tangential force applied at the rim brings the flywheel to a stop in \(15 \text{ s}\). The average torque exerted by the force is:
1. \(4~\text{N-m}\)
2. \(2~\text{N-m}\)
3. \(8~\text{N-m}\)
4. \(1~\text{N-m}\)
1. \(4~\text{N-m}\)
2. \(2~\text{N-m}\)
3. \(8~\text{N-m}\)
4. \(1~\text{N-m}\)
Subtopic: Â Rotational Motion: Dynamics |
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On a rotating wheel with a moment of inertia, \(2\) kg-m2 about its vertical axis, a torque that can stop the wheel's rotation in one minute is \(\dfrac{\mathit{\pi}}{15}~\text{N-m}\). The initial rotational speed of the wheel (in rpm) is:
| 1. | \(20\) | 2. | \(40\) |
| 3. | \(60\) | 4. | \(80\) |
Subtopic: Â Rotational Motion: Dynamics |
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Match the physical quantities listed in Column-I with their corresponding SI units given in Column-II.
Codes:
| Column-I | Column-II | ||
| \(\mathrm{(A)}\) | Angular velocity | \(\mathrm{(P)}\) | \(\text{J-s}\) |
| \(\mathrm{(B)}\) | Angular momentum | \(\mathrm{(Q)}\) | \(\text{N-m}\) |
| \(\mathrm{(C)}\) | Torque | \(\mathrm{(R)}\) | \(\text{kg-m}^2\) |
| \(\mathrm{(D)}\) | Moment of inertia | \(\mathrm{(S)}\) | \(\text{rad/s}\) |
| 1. | \(\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }\) |
| 2. | \(\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }\) |
| 3. | \(\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow Q, D \rightarrow S }\) |
| 4. | \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R} \) |
Subtopic: Â Rotational Motion: Dynamics |
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Level 1: 80%+
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A torque \(\tau\) acts on a body of moment of inertia \(I\) rotating with angular speed \(\omega.\) It will stop just after time:
| 1. | \(\dfrac{I \tau}{\omega}\) | 2. | \(\dfrac{I \omega}{\tau}\) |
| 3. | \(\dfrac{\tau \omega}{I}\) | 4. | \(I \omega \tau\) |
Subtopic: Â Rotational Motion: Dynamics |
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A force of \(54.4~\text{N}\) is applied on the free end of a string wrapped around a solid cylinder of mass \(15~\text{kg}\) and radius \(10~\text{cm}.\) What is the angular acceleration of the cylinder?
| 1. | \(94.10\) rad/s2 | 2. | \(72.5\) rad/s2 |
| 3. | \(14.50\) rad/s2 | 4. | \(94.50\) rad/s2 |
Subtopic: Â Rotational Motion: Dynamics |
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Given below are two statements:
Choose the correct option from the given ones:
1. (A) only
2. (B) only
3. both (A) and (B)
4. neither (A) nor (B)
| Statement A: | A body is in translational equilibrium if the net force on it is zero. |
| Statement B: | A body is in rotational equilibrium if the net torque about any point is zero. |
1. (A) only
2. (B) only
3. both (A) and (B)
4. neither (A) nor (B)
Subtopic: Â Rotational Motion: Dynamics |
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Level 1: 80%+
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A block with a mass of \(2\) kg is moving at a velocity of \(10\) m/s. It is connected to a string wound over a pulley (in the form of a disc) with a mass of \(2\) kg and a radius of \(0.1\) m, as shown in the figure. The angular speed of the pulley is:
(assume no slipping occurs)
1. \(10\) rad/s
2. \(100\) rad/s
3. \(0.1\) rad/s
4. \(0.01\) rad/s
(assume no slipping occurs)
1. \(10\) rad/s
2. \(100\) rad/s
3. \(0.1\) rad/s
4. \(0.01\) rad/s
Subtopic: Â Rotational Motion: Dynamics |
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When a force is applied to a rigid body, what happens to the distance between any two points on the body?
| 1. | It increases. | 2. | It decreases. |
| 3. | It remains constant. | 4. | It may either increase or decrease. |
Subtopic: Â Rotational Motion: Dynamics |
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Level 2: 60%+
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A uniform rod \(AB\) of length \(l\) and mass \(m\) is free to rotate about point \(A\). The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about \(A\) is \(\dfrac{ml^2}{3}\) the initial angular acceleration of the rod will be:
1. \(\dfrac{2g}{3l}\)
2. \(\dfrac{mgl}{2}\)
3. \(\dfrac{3}{2}gl\)
4. \(\dfrac{3g}{2l}\)
Subtopic: Â Rotational Motion: Dynamics |
 78%
Level 2: 60%+
AIPMT - 2007
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