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). |
(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. |
Assertion (A): | If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant. |
Reason (R): | The linear momentum of an isolated system remains constant. |
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): | The speed of a whirlwind in a tornado is alarmingly high. |
Reason (R): | If no external torque acts on a body, its angular velocity remains conserved. |
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. |
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. |
Assertion (A): | The centre of mass of an electron and proton when released moves faster towards the proton. |
Reason (R): | This is because the proton is heavier. |
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. |
Assertion (A): | For a system of particles under a central force field, the total angular momentum is conserved. |
Reason (R): | The torque acting on such a system is zero. |
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. |