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Q. No.The body of mass \(1.5\) kg rotating about an axis with angular velocity of \(0.3\) rad s-1 has the angular momentum of \(1.8\) kg m2s-1. The radius of gyration of the body about the axis is:
1.
\(2\) m
2.
\(1.2\) m
3.
\(0.2\) m
4.
\(1.6\) m
Subtopic: Angular Momentum |
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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 |
66%
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NEET - 2022
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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 |
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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 |
73%
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The ratio of the moments of inertia of two spheres about their diameter and having same mass and their radii in the ratio of \(1:2\) is:
1. \(2:1\)
2. \(4:1\)
3. \(1:2\)
4. \(1:4\)
Subtopic: Moment of Inertia |
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NEET - 2022
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A string is wrapped along the rim of a wheel of moment of inertia \(0.10\) kg-m2 and radius \(10\) cm. If the string is now pulled by a force \(10\) N, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2\) seconds is:
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s
Subtopic: Rotational Motion: Dynamics |
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From NCERT
NEET - 2022
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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 |
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Given below are two statements:
| Assertion (A): | 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 |
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A ring of mass of \(10\) kg and diameter of \(0.4\) m is rotated about its axis. If it makes \(2100\) revolutions per minute, then its angular momentum will be:
1. \(44 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
2. \(88 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
3. \(4.4 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
4. \(0.4 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
1. \(44 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
2. \(88 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
3. \(4.4 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
4. \(0.4 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\)
Subtopic: Angular Momentum |
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What is the value of linear velocity, if \(\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k} \text { and } \vec{r}=5 \hat{i}-6 \hat{j}+6 \hat{k}?\)
| 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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
Subtopic: Rotational Motion: Kinematics |
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