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Q. No.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. \(1.6~\text{m}\)
Subtopic: Angular Momentum |
86%
Level 1: 80%+
Hints
The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:
| 1. | \(1:\sqrt{2}\) | 2. | \(2:1\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(4:1\) |
Subtopic: Moment of Inertia |
68%
Level 2: 60%+
NEET - 2022
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 |
80%
Level 1: 80%+
Hints
The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of \(1:2\), is:
| 1. | \(2:1\) | 2. | \(4:1\) |
| 3. | \(1:2\) | 4. | \(1:4\) |
Subtopic: Moment of Inertia |
82%
Level 1: 80%+
NEET - 2022
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
What is the value of linear velocity, if the angular velocity vector is \(\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}\) and the position vector is \(\vec {r}=5 \hat{i}-6 \hat{j}+6 \hat{k}?\)
1. \(-18 \hat{i}-13 \hat{j}+2 \hat{k}\)
2. \(18 \hat{i}+13 \hat{j}-2 \hat{k}\)
3. \(6 \hat{i}+2 \hat{j}-3 \hat{k}\)
4. \(6 \hat{i}-2 \hat{j}+8 \hat{k}\)
1. \(-18 \hat{i}-13 \hat{j}+2 \hat{k}\)
2. \(18 \hat{i}+13 \hat{j}-2 \hat{k}\)
3. \(6 \hat{i}+2 \hat{j}-3 \hat{k}\)
4. \(6 \hat{i}-2 \hat{j}+8 \hat{k}\)
Subtopic: Rotational Motion: Kinematics |
75%
Level 2: 60%+
Hints
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