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Q. No.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 |
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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 |
79%
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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 |
74%
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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 |
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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 |
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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 |
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The radius of gyration of a cylindrical rod of length \(10 \sqrt 3\) m about an axis of rotation perpendicular to its length and passing through the center will be:
1. \(5\) m
2. \(3\) m
3. \(1\) m
4. \(4\) m
1. \(5\) m
2. \(3\) m
3. \(1\) m
4. \(4\) m
Subtopic: Moment of Inertia |
85%
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The ratio of the radius of gyration of a circular disc to that of a circular ring, both having the same mass and radius, about their respective axes is:
| 1. | \(\sqrt2:\sqrt3\) | 2. | \(\sqrt3:\sqrt2\) |
| 3. | \(1:\sqrt2\) | 4. | \(\sqrt2:1\) |
Subtopic: Moment of Inertia |
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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 \(2\pi~\text {rad/s}\) to \(\pi~\text {rad/s}\) in \(10~\text {s}.\) If the moment of inertia of the ball is \(0.5~\text{kg/m}^2,\) the torque acting on the ball is:
| 1. | \(-\frac{\pi}{100} ~\text{N-m}\) | 2. | \(-\frac{\pi}{50} ~\text{N-m}\) |
| 3. | \(-\frac{\pi}{20} ~\text{N-m}\) | 4. | \(-\frac{\pi}{10}~\text{N-m}\) |
Subtopic: Torque |
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An energy of \(484~\text J\) is spent in increasing the speed of a flywheel from \(60~\text{rpm}\) to \(360~\text{rpm}.\) The moment of inertia of the flywheel is:
| 1. | \(0.7~\text{kg-m}^2\) | 2. | \(3.22~\text{kg-m}^2\) |
| 3. | \(30.8~\text{kg-m}^2\) | 4. | \(0.07~\text{kg-m}^2\) |
Subtopic: Moment of Inertia |
58%
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