# 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 |
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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 |
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Given below are two statements:
 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.
Subtopic: Â Torque |
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Given below are two statements:
 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.
Subtopic: Â Torque |
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Given below are two statements:
 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.
Subtopic: Â Angular Momentum |
Â 77%
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Given below are two statements:
 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.
Subtopic: Â Center of Mass |
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Given below are two statements:
 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.
Subtopic: Â Angular Momentum |
Â 84%
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Given below are two statements:
 Assertion (A): If the ice cap of the pole melts, the day length will shorten. Reason (R): Ice flows towards the equator and decreases the moment of inertia of the earth. This increases the frequency of rotation of the earth.

 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 Angular Momentum |
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