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Q. No.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): | 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%
From NCERT
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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 |
77%
From NCERT
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What is the value of linear velocity, if \(\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k} \text { and } \vec{r}=5 \hat{i}-6 \hat{j}+6 \hat{k} \text { ? }\)
| 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 |
68%
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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 |
86%
From NCERT
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The ratio of radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axis is:
1. \(\sqrt2:\sqrt3\)
2. \(\sqrt3:\sqrt2\)
3. \(1:\sqrt2\)
4. \(\sqrt2:1\)
1. \(\sqrt2:\sqrt3\)
2. \(\sqrt3:\sqrt2\)
3. \(1:\sqrt2\)
4. \(\sqrt2:1\)
Subtopic: Moment of Inertia |
87%
From NCERT
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A ball is spinning on a horizontal surface, about the vertical axis passing through its center. 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 |
87%
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An energy of \(484\) J is spent in increasing the speed of a flywheel from \(60\) rpm to \(360\) rpm. The moment of inertia of the flywheel is:
1. \(0.7\) kg-m2
2. \(3.22\) kg-m2
3. \(30.8\) kg-m2
4. \(0.07\) kg-m2
1. \(0.7\) kg-m2
2. \(3.22\) kg-m2
3. \(30.8\) kg-m2
4. \(0.07\) kg-m2
Subtopic: Moment of Inertia |
57%
From NCERT
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The moment of inertia of a uniform circular disc of radius \(R\) and mass \(M\) about an axis passing through the centre and perpendicular to its plane is:
1. \(\frac14MR^2\)
2. \(\frac12MR^2\)
3. \(MR^2\)
4. \(\frac32MR^2\)
1. \(\frac14MR^2\)
2. \(\frac12MR^2\)
3. \(MR^2\)
4. \(\frac32MR^2\)
Subtopic: Moment of Inertia |
84%
From NCERT
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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 |
78%
From NCERT
NEET - 2022
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