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Q. No.A string is wrapped along the rim of a wheel of the 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 \(2\) s is:
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s
1. \(40\) rad/s
2. \(80\) rad/s
3. \(10\) rad/s
4. \(20\) rad/s
Subtopic: Rotational Motion: Dynamics |
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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 |
72%
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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 |
63%
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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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Given the angular velocity vector \(\overrightarrow{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}\) and the position vector \(\overrightarrow {r}=5 \hat{i}-6 \hat{j}+6 \hat{k},\) what is the linear velocity?
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 |
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A ball is spinning on a horizontal surface, about the vertical axis passing through its centre. Its angular velocity decreases from \(2\pi\) rad/s to \(\pi\) rad/s in \(10\) s. If the moment of inertia of the ball is \(0.5\) kg-m2, the torque acting on the ball is:
1. \(-\frac{\pi}{100} \) N-m
2. \(-\frac{\pi}{50} \) N-m
3. \(-\frac{\pi}{20} \) N-m
4. \(-\frac{\pi}{10}\) N-m
1. \(-\frac{\pi}{100} \) N-m
2. \(-\frac{\pi}{50} \) N-m
3. \(-\frac{\pi}{20} \) N-m
4. \(-\frac{\pi}{10}\) N-m
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 |
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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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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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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. \(\frac{2}{5}mv_{0}R\)
2. \(\frac{1}{5}mv_{0}R\)
3. \(\frac{7}{5}mv_{0}R\)
4. \(mv_{0}R\)
1. \(\frac{2}{5}mv_{0}R\)
2. \(\frac{1}{5}mv_{0}R\)
3. \(\frac{7}{5}mv_{0}R\)
4. \(mv_{0}R\)
Subtopic: Angular Momentum |
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