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Q. No.What is the centre of gravity of semi-circular disc of radius \((R)\)?
1. \(2R \over \pi\)
2. \(4R \over 3\pi\)
3. \(R \over 2\)
4. \(3R \over 8\)
Subtopic: Center of Mass |
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A force of \(54.4~\text{N}\) is applied on the free end of a string wrapped around a solid cylinder of mass \(15~\text{kg}\) and radius \(10~\text{cm}.\) What is the angular acceleration of the cylinder?
| 1. | \(94.10\) rad/s2 | 2. | \(72.5\) rad/s2 |
| 3. | \(14.50\) rad/s2 | 4. | \(94.50\) rad/s2 |
Subtopic: Rotational Motion: Dynamics |
82%
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JEE
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What is the displacement of point \(A\) on the top of the disc rolling without slipping on horizontal surface with angular speed \(\omega\), in half rotation?
1. \(R \sqrt{\pi^2+2} \)
2. \(R \sqrt{\pi^2+\frac{1}{4}} \)
3. \(R \sqrt{\pi^2+4} \)
4. \(R \sqrt{\frac{\pi^2}{2}+1}\)
1. \(R \sqrt{\pi^2+2} \)
2. \(R \sqrt{\pi^2+\frac{1}{4}} \)
3. \(R \sqrt{\pi^2+4} \)
4. \(R \sqrt{\frac{\pi^2}{2}+1}\)
From NCERT
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Solid sphere rolls on horizontal plane. Ratio of angular momentum about COM to total energy is \(\pi \over 22\). The angular velocity of the solid sphere in (rad/s) is:
1. \(4\)
2. \(3\)
4. \(2\)
4. \(1\)
1. \(4\)
2. \(3\)
4. \(2\)
4. \(1\)
Subtopic: Angular Momentum |
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JEE
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The moment of inertia of a semi-circular ring of mass \(M\) and radius \(R\) about an axis passing through the centre and perpendicular to the plane of the ring is:
1. \(MR^2\)
2. \(\dfrac{1}{2}MR^2\)
3. \(2MR^2\)
4. \(\dfrac{3}{4}MR^2\)
1. \(MR^2\)
2. \(\dfrac{1}{2}MR^2\)
3. \(2MR^2\)
4. \(\dfrac{3}{4}MR^2\)
Subtopic: Moment of Inertia |
61%
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JEE
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Momentum of a particle is increased by 50% by keeping its mass constant. Percentage increase in kinetic energy of particle is:
1. 50%
2. 125%
3. 100%
4. 200%
1. 50%
2. 125%
3. 100%
4. 200%
Subtopic: Linear Momentum |
83%
From NCERT
JEE
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A solid sphere and a ring have equal masses and equal radii of gyration. If the sphere is rotating about its diameter and the ring about an axis passing through and perpendicular to its plane, then the ratio of the radii is \(\sqrt{\dfrac{x}{2}}.\) The value of \(x\) is:
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
1. \(5\)
2. \(2\)
3. \(1\)
4. \(4\)
Subtopic: Moment of Inertia |
85%
From NCERT
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A body of mass 5 kg has the linear momentum of \(100 ~kg~ ms^{-1}\) and acted upon by the force of 2 N for 2 seconds, then change in kinetic energy in Joule is:
1. 100 J
2. 90 J
3. 204 J
4. 81.6 J
1. 100 J
2. 90 J
3. 204 J
4. 81.6 J
Subtopic: Linear Momentum |
68%
From NCERT
JEE
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What is the ratio of the radius of gyration of a solid sphere to that of a solid cylinder, given that both objects have the same mass and radius?
| 1. | \(\dfrac{2}{\sqrt{5}}\) | 2. | \(\dfrac{\sqrt{5}}{2}\) |
| 3. | \(\sqrt{\dfrac{2}{5}}\) | 4. | \(\dfrac{2}{\sqrt{3}}\) |
Subtopic: Moment of Inertia |
77%
From NCERT
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Earth shrinks to \(1 \over 64\) times of its initial volume. Time period of earth rotation is found to be \( {24 \over x }~ \text {hrs.}\) The value of \(x\) is:
1. \(16\)
2. \(20\)
3. \(4\)
4. \(10\)
1. \(16\)
2. \(20\)
3. \(4\)
4. \(10\)
Subtopic: Angular Momentum |
52%
JEE
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