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Q. No.A uniform rod on a smooth horizontal table is moving with uniform horizontal speed \(v.\) Suddenly rod is hinged at the centre of the rod. The angular velocity of the rod, now, will be:
1.
\(\dfrac{2v}{3l}\)
2.
\(\dfrac{3v}{2l}\)
3.
\(\dfrac{v}{l}\)
4.
zero
Subtopic: Angular Momentum |
61%
Level 2: 60%+
Hints
A solid sphere of mass \(m\) is in pure rolling motion with the centre of mass moving with velocity \(v_{0}.\) It's angular momentum about the point \(P\) shown in the diagram is:
| 1. | \(\dfrac{2}{5}mv_{0}R\) | 2. | \(\dfrac{1}{5}mv_{0}R\) |
| 3. | \(\dfrac{7}{5}mv_{0}R\) | 4. | \(mv_{0}R\) |
Subtopic: Angular Momentum |
75%
Level 2: 60%+
Hints
The body of mass \(1.5~\text{kg}\) rotating about an axis with angular velocity of \(0.3~\text{rad s}^{-1}\) has the angular momentum of \(1.8~\text{kg m}^2\text{s}^{-1}\). The radius of gyration of the body about the axis is:
1. \(2~\text{m}\)
2. \(1.2~\text{m}\)
3. \(0.2~\text{m}\)
4. \(1.6~\text{m}\)
1. \(2~\text{m}\)
2. \(1.2~\text{m}\)
3. \(0.2~\text{m}\)
4. \(1.6~\text{m}\)
Subtopic: Angular Momentum |
86%
Level 1: 80%+
Hints
A uniform rod of mass \(m\) and length \(l\) is in uniform translational motion. If one of its ends is suddenly hinged, then (hinge is smooth):
| 1. | It will continue its translational motion. |
| 2. | It will now be in pure rotational motion about the hinged end. |
| 3. | It will now have combined translational and rotational motion. |
| 4. | It will stop. |
Subtopic: Angular Momentum |
72%
Level 2: 60%+
Hints
Given below are two statements:
| Assertion (A): | If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant. |
| Reason (R): | The linear momentum of an isolated system remains constant. |
| 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 True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Torque |
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | If the ice on the polar caps of the earth melts, then the length of the day will increase. |
| Reason (R): | Moment of inertia of the earth increases, as ice on polar caps melts. |
| 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 True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Angular Momentum |
79%
Level 2: 60%+
Hints
A string is wrapped along the rim of a wheel of the moment of inertia \(0.10~\text{kg-m}^2\) and radius \(10~\text{cm}.\) If the string is now pulled by a force of \(10~\text N,\) then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2~\text s\) will be:
| 1. | \(40~\text{rad/s}\) | 2. | \(80~\text{rad/s}\) |
| 3. | \(10~\text{rad/s}\) | 4. | \(20~\text{rad/s}\) |
Subtopic: Rotational Motion: Dynamics |
80%
Level 1: 80%+
NEET - 2022
Hints
Given below are two statements:
| Assertion (A): | For a body under translatory as well as rotational equilibrium, net torque about any axis is zero. |
| Reason (R): | Together \( \Sigma \vec{F}_{i}=0 \text { and } \Sigma\left(\vec{r}_{i} \times \vec{F}_{i}\right)=0 \) implies that \( \Sigma\left(\vec{r}_{i}-\overrightarrow{r_{0}}\right) \times \vec{F}=0 \). |
| 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 True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Rotational Motion: Dynamics |
75%
Level 2: 60%+
Hints
Given below are two statements:
| Assertion (A): | The axis of rotation of a rigid body cannot lie outside the body. |
| Reason (R): | It must pass through a material particle of the body. |
| 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 True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Rotational Motion: Kinematics |
72%
Level 2: 60%+
Hints
A ring of mass of \(10~\text{kg}\) and diameter of \(0.4~\text m\) is rotated about its axis. If it makes \(2100\) revolutions per minute, then its angular momentum will be:
1. \(44~\text{kg m}^{2} \text{s}^{-1}\)
2. \(88 ~\text{kg m}^{2} \text{s}^{-1}\)
3. \(4.4~\text{kg m}^{2} \text{s}^{-1}\)
4. \(0.4~\text{kg m}^{2} \text{s}^{-1}\)
1. \(44~\text{kg m}^{2} \text{s}^{-1}\)
2. \(88 ~\text{kg m}^{2} \text{s}^{-1}\)
3. \(4.4~\text{kg m}^{2} \text{s}^{-1}\)
4. \(0.4~\text{kg m}^{2} \text{s}^{-1}\)
Subtopic: Angular Momentum |
81%
Level 1: 80%+
Hints
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