# 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

Subtopic: Â Center of Mass |
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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.

Subtopic: Â Center of Mass |
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Given below are two statements:
 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.
Subtopic: Â Angular Momentum |
Â 57%
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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.
Subtopic: Â Torque |
Â 80%
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Consider the following statements.
 A: A body is in translational equilibrium if the net force on it is zero. B: A body is in rotational equilibrium if the net torque about any point is zero.
Choose the correct statements:
 1 (A) only 2 (B) only 3 both (A) and (B) 4 neither (A) nor (B)
Subtopic: Â Rotational Motion: Dynamics |
Â 80%
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Given below are two statements:
 Assertion (A): The center 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 center 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).
Subtopic: Â Center of Mass |
Â 75%
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A uniform rod of mass $$M$$ and length $$L$$ lies at rest on a smooth horizontal plane, as shown in the figure. A particle of mass $$m,$$ moving with an initial velocity $$u$$ strikes one end $$(A)$$ of the rod and stops. The initial velocity $$u$$ is perpendicular to the length $$(AB)$$ of the rod.

Consider the following statements:
 P. Momentum of the system is conserved. Q. Kinetic energy of the system does not change after the collision. R. Angular momentum of the system is conserved.

1. P, Q, R are true.
2. P, R are true.
3. Only R is true.
4. Only P is true.
Subtopic: Â Angular Momentum |
Â 50%
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A block of mass $$m$$ is placed atop another block of mass $$M,$$ and the combination is at rest on a smooth horizontal table. A force $$F_1$$ is applied to $$m$$ and another force $$F_2$$ is applied to $$M,$$ the two acting horizontally and in opposite directions. Consider the following statements about the acceleration $$(a_{cm})$$ of the centre of mass of the system). (Take right as positive)

 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

Choose the most appropriate option:
 1 only (A) is true. 2 only (B) is true. 3 (C) is true. 4 (A), (B) are true but (C) is false.
Subtopic: Â Center of Mass |
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Given below are two statements:
 Assertion (A): The angular momentum of system always remains constant. Reason (R): For a system, $$\tau_{ext} = {dL \over dt} = 0$$

 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.
Subtopic: Â Angular Momentum |
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Given below are two statements:
 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.
Subtopic: Â Torque |
Â 80%
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