Q. No.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. \(\vec{\tau}=5(1-\sqrt{3}) \hat{k}\) 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
Four thin rods, each of mass m and length L, form a square. The moment of inertia on any side of the square is:
1.
2.
3.
4.
| 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.
A bomb is projected from the ground at a horizontal range of R. If the bomb explodes mid-air, then the range of its centre of mass is:
1.
2.
3.
4.
The law of conservation of angular momentum is valid when:
| 1. | The net force is zero and the net torque is non-zero | 2. | The net force is non-zero and the net torque is non zero |
| 3. | Net force may or may not be zero and net torque is zero | 4. | Both force and torque must be zero |
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