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: Center of Mass |

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Q13:

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: Angular Momentum |

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Q14:

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: Torque |

80%

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Q15:

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: Torque |

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Q16:

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: Torque |

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Q17:

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: Angular Momentum |

77%

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Q18:

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: Center of Mass |

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Q19:

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: Angular Momentum |

84%

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Q20:

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: Angular Momentum |

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Q21:

Given below are two statements:

Assertion (A):	The centre of mass of a two-particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason (R):	The product of the mass of one particle and its distance from the centre of mass is numerically equal to the product of the mass of another particle and its distance from the centre of mass.

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: Center of Mass |

67%

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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

1.	only (A) is true.
2.	only (B) is true.
3.	(C) is true.
4.	(A), (B) are true but (C) is false.

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