Q. No.A particle starting from rest moves in a circle of radius \(r\). It attains a velocity of \(v_0~\text{m/s}\) on completion of \(n\) rounds. Its angular acceleration will be:
1.
\( \dfrac{v_0}{n} ~\text{rad} / \text{s}^2\)
2.
\( \dfrac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \)
3.
\( \dfrac{v_0^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \)
4.
\( \dfrac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \)
A disc of radius \(2~\text{m}\) and mass \(100~\text{kg}\) rolls on a horizontal floor. Its centre of mass has a speed of \(20~\text{cm/s}\). How much work is needed to stop it?
| 1. | \(1~\text{J}\) | 2. | \(3~\text{J}\) |
| 3. | \(30~\text{J}\) | 4. | \(2~\text{J}\) |
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6~\text{N-m}\)
2. \(2\times 10^{-6}~\text{N-m}\)
3. \(2\times 10^{-3}~\text{N-m}\)
4. \(12\times 10^{-4}~\text{N-m}\)
Two particles of mass \(5~\text{kg}\) and \(10~\text{kg}\) respectively are attached to the two ends of a rigid rod of length \(1~\text{m}\) with negligible mass. The centre of mass of the system from the \(5~\text{kg}\) particle is nearly at a distance of:
1. \(50~\text{cm}\)
2. \(67~\text{cm}\)
3. \(80~\text{cm}\)
4. \(33~\text{cm}\)
What would be the torque about the origin when a force \(3\hat{j}~\text N\) acts on a particle whose position vector is \(2\hat{k}~\text m?\)
| 1. | \(6\hat{j}~\text{N-m}\) | 2. | \(-6\hat{i}~\text{N-m}\) |
| 3. | \(6\hat{k}~\text{N-m}\) | 4. | \(6\hat{i}~\text{N-m}\) |
The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)
| 1. | \(2(\hat{i}+\hat{j})\) | 2. | \(\hat{i}+\hat{j}\) |
| 3. | \(\frac{2}{3}(\hat{i}+\hat{j})\) | 4. | \(\frac{4}{3}(\hat{i}+\hat{j})\) |
From a circular ring of mass \({M}\) and radius \(R,\) an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2.\) The value of \(K\) will be:
| 1. | \(\frac{1}{4}\) | 2. | \(\frac{1}{8}\) |
| 3. | \(\frac{3}{4}\) | 4. | \(\frac{7}{8}\) |
A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium?
(Take \(g=10~( \text {m/s}^2)\)
| 1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
| 3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
| 1. | \(5~ \text m\) | 2. | \(\dfrac{10}{3} \mathrm{~m}\) |
| 3. | \(\dfrac{20}{3} \mathrm{~m}\) | 4. | \(10~ \text m\) |
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