Q. No.The moment of inertia of a uniform ring of mass \(M\) and radius \(R,\) about a tangent to the ring, is:
1.
\(\dfrac{1}{2}MR^2\)
2.
\(MR^2\)
3.
\(\dfrac{3}{2}MR^2\)
4.
\(2MR^2\)
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| 1. | \(\dfrac12MRv\) | 2. | \(\dfrac23MRv\) |
| 3. | \(\dfrac25MRv\) | 4. | \(\dfrac27MRv\) |
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| 1. | \(\dfrac{1}{12}Mv^2\) | 2. | \(\dfrac{1}{3}Mv^2\) |
| 3. | \(\dfrac{1}{6}Mv^2\) | 4. | \(\dfrac{2}{3}Mv^2\) |
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The angular acceleration \((\alpha)\) of the disc is:
| 1. | \(\dfrac{F}{2MR}\) | 2. | \(\dfrac{F}{MR}\) |
| 3. | \(\dfrac{2F}{MR}\) | 4. | \(\dfrac{3F}{2MR}\) |
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The time taken to complete a revolution is:
| 1. | \(\begin{aligned}\sqrt{\dfrac{4\pi MR}{F}} \\ \end{aligned}\) | 2. | \(\begin{aligned}\sqrt{\dfrac{2\pi MR}{F}} \\ \end{aligned}\) |
| 3. | \(\begin{aligned}\sqrt{\dfrac{ MR}{F}} \\ \end{aligned}\) | 4. | \(\begin{aligned}\sqrt{\dfrac{MR}{2\pi F}} \\ \end{aligned}\) |
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The work done by the force is:
1. \(F\cdot 2\pi\)
2. \(F\cdot R\)
3. \(F\cdot \pi R\)
4. \(F\cdot 2\pi R\)
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| Assertion (A): | The kinetic energies of two identical particles of a rotating rigid body are proportional to the square of their respective distances from the axis of rotation. |
| Reason (R): | The kinetic energy of a particle is \(\Large\frac12\)\(mv^2,\) while the velocity \(v\) is proportional to the distance from the axis of rotation \(\text{(}r\text{):} \) \(v=\omega r, \) \(\omega\) is the angular speed. |
| 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. |
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| 1. | is closer to \(A,\) centre of the sphere |
| 2. | is closer to \(B,\) centre of the cylinder |
| 3. | is at the mid-point of \(A\) and \(B\) |
| 4. | cannot be determined from the information given |
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| 1. | \(6~\text{cm}\) | 2. | \(10~\text{cm}\) |
| 3. | \(12~\text{cm}\) | 4. | \(14~\text{cm}\) |
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| 1. | \(v\) | 2. | \(2v\) |
| 3. | \(\dfrac{v}{2}\) | 4. | zero |
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