A wheel has an angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2 s,
it has rotated through an angle (in radian) of:
1. 6
2. 10
3. 12
4. 4
An electric fan rotating at 1200 rpm is switched off. If the fan stops after 10 seconds, the number of revolutions completed by the fan before it stops will be: (assume uniform retardation)
1. | 100 | 2. | 50 |
3. | 40 | 4. | 20 |
For a rigid body rotating about a fixed axis, which of the following quantities is the same at an instant for all the particles of the body?
1. | Angular acceleration |
2. | Angular velocity |
3. | Angular displacement in the given time interval |
4. | All of these |
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. \(-5\hat{i}-2\hat{j}-3\hat{k}\)
If a body is moving in a circular path with decreasing speed, then: (symbols have their usual meanings):
1.
2.
3.
4. All of these
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 rigid body rotates about a fixed axis with a variable angular velocity equal to \(\alpha\) \(-\) \(\beta t\), at the time t, where \(\alpha , \beta\) are constants. The angle through which it rotates before it stops is:
1. | \(\frac{\left(\alpha\right)^{2}}{2 \beta}\) | 2. | \(\frac{\left(\alpha\right)^{2} - \left(\beta\right)^{2}}{2 \alpha}\) |
3. | \(\frac{\left(\alpha\right)^{2} - \left(\beta\right)^{2}}{2 \beta}\) | 4. | \(\frac{\left(\alpha-\beta\right) \alpha}{2}\) |
Particles A and B are separated by 10 m, as shown in the figure. If A is at rest and B started moving with a speed of 20 m/s then the angular velocity of B with respect to A at that instant is:
1. | 1 rad s-1 | 2. | 1.5 rad s-1 |
3. | 2 rad s-1 | 4. | 2.5 rad s-1 |
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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
Two gear wheels that are meshed together have radii of 0.50 cm and 0.15 cm. The number of revolutions made by the smaller one when the larger one goes through 3 revolutions is:
1. 5 revolutions
2. 20 revolutions
3. 1 revolution
4. 10 revolutions