1. | \(2\) | 2. | \(12\) |
3. | \(6\) | 4. | \(3\) |
Assertion (A): | The centre-of-mass of an isolated system of particles remains at rest if it is initially at rest. |
Reason (R): | Internal forces acting within a system cannot change the velocity of the centre-of-mass which is proportional to the total momentum of the system. |
1. | (A) is True but (R) is False. |
2. | (A) is False but (R) is True. |
3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
1. | \(104 \pi\) | 2. | \(2\pi\) |
3. | \(4\pi\) | 4. | \(12\pi\) |
The ratio of the moments of inertia of two spheres, about their diameters, having the same mass and their radii being in the ratio of \(1:2\), is:
1. | \(2:1\) | 2. | \(4:1\) |
3. | \(1:2\) | 4. | \(1:4\) |
A string is wrapped along the rim of a wheel of the moment of inertia \(0.10~\text{kg-m}^2\) and radius \(10~\text{cm}.\) If the string is now pulled by a force of \(10~\text N,\) then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after \(2~\text s\) will be:
1. | \(40~\text{rad/s}\) | 2. | \(80~\text{rad/s}\) |
3. | \(10~\text{rad/s}\) | 4. | \(20~\text{rad/s}\) |
Assertion (A): | If polar ice melts, days will be longer. |
Reason (R): | Moment of inertia increases and thus angular velocity decreases. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
1. | \(12\) | 2. | \(14\) |
3. | \(16\) | 4. | \(18\) |