Given below are two statements:
Assertion (A): | Angular momentum of an isolated system of particles is conserved. |
Reason (R): | The net torque on an isolated system of particles is zero and the rate of change of angular momentum equals the torque. |
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. | (A) is False but (R) is True. |
Assertion (A): | If the sun were to 'suddenly' be removed, then the earth would continue to move around in its orbit. |
Reason (R): | Angular momentum of a system of particles is conserved when there is no external torque. |
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. | (A) is False but (R) is True. |
Statement A: | A body is in translational equilibrium if the net force on it is zero. |
Statement B: | A body is in rotational equilibrium if the net torque about any point is zero. |
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). |
Consider the following two statements:
A: | The linear momentum of a system of particles is zero. |
B: | The kinetic energy of a system of particles is zero. |
1. | A implies B and B implies A. |
2. | A does not imply B and B does not imply A. |
3. | A implies B but B does not imply A. |
4. | B implies A but A does not imply B. |
Consider the following two statements:
A: | The linear momentum of the system remains constant. |
B: | The centre of mass of the system remains at rest. |
1. | A implies B and B implies A |
2. | A does not imply B and B does not imply A |
3. | A implies B but B does not imply A |
4. | B implies A but A does not imply B |
(P) | The momentum of the system is conserved. |
(Q) | The kinetic energy of the system does not change after the collision. |
(R) | The angular momentum of the system is conserved. |
1. | P, Q, and R are true. |
2. | P and R are true. |
3. | Only R is true. |
4. | Only P is true. |
(A) | \(a_{cm}=\dfrac{F_1-F_2}{m+M},\) if there is no friction acting between \(m\) and \(M\) |
(B) | \(a_{cm}=\dfrac{F_1-F_2}{m+M},\) if there is static friction between \(m\) and \(M\) |
(C) | \(a_{cm}=\dfrac{F_1-F_2}{m+M},\) in all situations |
Assertion (A): | The angular momentum of system always remains constant. |
Reason (R): | \(\tau_{ext} = {dL \over dt} = 0\) | For a system,
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. | (A) is False but (R) is True. |
Assertion (A): | A ladder is more apt to slip when you are high up on it than when you just begin to climb. |
Reason (R): | At high up on a ladder, the torque is large and on climbing up, the torque is small. |
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. |