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 |
A body of mass M is moving on a circular track of radius r in such a way that its kinetic energy K depends on the distance travelled by the body s according to relation K = s, where is a constant. The angular acceleration of the body is:
1.
2.
3.
4.
If a particle moves in a circle with a constant angular speed () about point O, then its angular speed about point A will be:
1. 2
2.
3.
4.
Which of the following is the value of the torque of force \(F\) about origin \(O:\)
1. \(\vec{\tau}=5(1-\sqrt{3}) \hat{k}\) N-m
2. \(\vec{\tau}=5(1-\sqrt{3}) \hat{j}\) N-m
3. \(\vec{\tau}=5(\sqrt{3}-1) \hat{i}\) N-m
4. \(\vec{\tau}=\sqrt{3} \hat{j}\) N-m
1. | \(\vec{\tau}=(-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}})\) N-m |
2. | \(\vec{\tau}=(-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-4 \widehat{\mathrm{k}}) \) N-m |
3. | \(\vec{\tau}=(17 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}})\) N-m |
4. | \(\vec{\tau}=(-41 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+16 \hat{\mathrm{k}})\) N-m |
In the three figures, each wire has a mass M, radius R and a uniform mass distribution. If they form part of a circle of radius R, then about an axis perpendicular to the plane and passing through the centre (shown by crosses), their moment of inertia is in the order:
1.
2.
3.
4.
A solid body rotates about a stationary axis according to the equation . What is the average angular velocity over the time interval between t = 0 and the time when the body comes to rest? ( : angular displacements, t : time)
1. | 1 rad/s | 2. | 2 rad/s |
3. | 3 rad/s | 4. | 4 rad/s |
The value of M, as shown, for which the rod will be in equilibrium is:
1. | 1 kg | 2. | 2 kg |
3. | 4 kg | 4. | 6 kg |
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 |
A uniform cubical block of side L rests on a rough horizontal surface with coefficient of friction . A horizontal force F is applied on the block as shown. If there is sufficient friction between the block and the ground, then the torque due to normal reaction about its centre of mass is:
1.
2.
3.
4.