A uniform rod of length l is hinged at one end and is free to rotate in the vertical plane. The rod is released from its position, making an angle with the vertical. The acceleration of the free end of the rod at the instant it is released is:
1. | \(\frac{3 g \sin \theta}{4} \) | 2. | \(\frac{3 g \cos \theta}{2} \) |
3. | \(\frac{3 g \sin \theta}{2} \) | 4. | \(\frac{3 g \cos \theta}{4}\) |
On a rough horizontal surface (coefficient of friction ), a cubical block of side 'a' and mass m is projected horizontally. The net torque on the block about its centre of mass till the block stops is equal to:
1. zero
2.
3. mga
4. mga
An insect, initially on the circumference of a disc, starts moving along a chord of the disc, rotating about an axis passing through the center and perpendicular to the plane of the disc. Its angular speed:
1. | increases. | 2. | decreases. |
3. | first increases then decreases. | 4. | first decreases then increases. |
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 \((\omega)\) about point \(O\), then its angular speed about point \(A\) will be:
1. \(2\omega\)
2. \(\frac{\omega}{2}\)
3. \(\omega\)
4. \(\frac{\omega}{4}\)
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. \(\frac{5}{3}mL^2\)
2. \(4mL^2\)
3. \(\frac{1}{4}mL^2\)
4. \(\frac{2}{3}mL^2\)
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.