- 1(current)
Q. No.| 1. | along the axis of rotation |
| 2. | along the radius, away from centre |
| 3. | along the radius towards the centre |
| 4. | along the tangent to its position |
1. \(1\) rad/s
2. \(5\) rad/s
3. \(10\) rad/s
4. \(15\) rad/s
1. \(104 \pi\)
2. \(2\pi\)
3. \(4\pi\)
4. \(12\pi\)
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. | \(1 ~\text{rad/s}^2\) |
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. | \( \frac{v_0}{n} ~\text{rad} / \text{s}^2\) | 2. | \( \frac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \) |
| 3. | \( \frac{v_o^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \) | 4. | \( \frac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \) |
Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass \(\mathrm{M}\) and radius \(\mathrm{R}.\) They all spin with the same angular speed about their own symmetry axes. The amount of work (\(\mathrm{W}\)) required to bring them to rest, would satisfy the relation:
| 1. | \(\mathrm{W_C}>\mathrm{W_B}>\mathrm{W_A} ~~~~~~~~\) |
| 2. | \(\mathrm{W_A}>\mathrm{W_B}>\mathrm{W_C}\) |
| 3. | \(\mathrm{W_B}>\mathrm{W_A}>\mathrm{W_C}\) |
| 4. | \(\mathrm{W_A}>\mathrm{W_C}>\mathrm{W_B}\) |
A solid sphere of mass \(m\) and radius \(R\) is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (sphere/cylinder) will be:
| 1. | \(2:3\) | 2. | \(1:5\) |
| 3. | \(1:4\) | 4. | \(3:1\) |
\(\theta(t)=2t^{3}-6t^{2}\)
The torque on the wheel becomes zero at:
1. \(t=0.5\) s
2. \(t=0.25\) s
3. \(t=2\) s
4. \(t=1\) s
A wheel has an angular acceleration of \(3.0\) rad/s2 and an initial angular speed of \(2.0\) rad/s. In a time of \(2\) s, it has rotated through an angle (in radians) of:
| 1. | \(6\) | 2. | \(10\) |
| 3. | \(12\) | 4. | \(4\) |
For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\) and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\) its velocity will be:
1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)
2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)
3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)
4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)
- 1(current)
Q. No.
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