Assertion (A): The work done during a round trip is always zero.
Reason (R): No force is required to move a body in its round trip.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Work done by conservative forces in a closed loop is zero. For all forces, it depends on energy change and non-conservative forces. Force is required to move a body, especially to overcome inertia or friction. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): An athlete accelerates from rest to its maximum speed due to friction between his shoes and track.
Reason (R): Positive work done by frictional force increases the kinetic energy of athlete.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion is true: An athlete pushes backward on the ground, and the ground exerts a forward static friction force on the athlete, causing acceleration.
Reason is true: The static friction force acts in the direction of the athlete's motion. Therefore, it does positive work, which directly increases the athlete's kinetic energy \(K\) according to the work-energy theorem.
Both A and R are true, and R provides the correct explanation for A.
Assertion (A): Net work done by all the internal force of a system is independent of choice of reference frame.
Reason (R): Value of force is independent of choice of reference frame.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Work done by internal forces depends on relative displacement (\(\Delta \vec{r}\)) which is frame-independent, so (A) is true.
The value of a force is generally not independent of the reference frame, especially if non-inertial frames are considered, so (R) is false.
Assertion (A): Work done by a force is always same in all inertial frame of references.
Reason (R): Work is an invariant physical quantity.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Work done (\(W = \vec{F} \cdot \vec{d}\)) depends on displacement (\(\vec{d}\)) which is frame-dependent in different inertial frames. Therefore, work is not always the same and is not an invariant quantity. Both Assertion and Reason are false.
Assertion (A): Work done is positive when force acts in the direction of displacement.
Reason (R): Work done by frictional force can not be positive.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Work is \(W = \vec{F} \cdot \vec{d} = Fd cos\theta\). If \(theta = 0\), \(W\) is positive, so (A) is true. Frictional force always opposes motion, so work done by it is negative or zero, never positive. So (R) is true. However, (R) does not explain (A).
Assertion (A): A particle is rotated in a vertical circle with the help of a string. Work done by tension in the string on particle is zero.
Reason (R): Tension is always perpendicular to instantaneous velocity.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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In circular motion, tension acts as the centripetal force, directed towards the center, while velocity is tangential. Thus, tension is always perpendicular to velocity (\(\theta = 90^\circ\)), meaning work done (\(W = Fd cos 90^\circ\)) is zero. Both are true, and Reason explains Assertion.
Assertion (A): Karnam Malleshwari famous Indian weight lifter lifts a weight up and returns it to same initial position along the same path. Net work done by muscles of weight lifter is positive.
Reason (R): Net displacement of weight is zero.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The weight starts and ends at the same position, so its net displacement is \(0\). Thus, Reason (R) is true. If the weight starts and ends at rest, \(\Delta K = 0\) for the weight. By Work-Energy Theorem, \(W_{\text{net}} = \Delta K\), so \(W_{\text{net}} = 0\). This implies the net work done by muscles is also zero, as gravity does zero net work over a round trip. So, Assertion (A) is false.
Assertion (A): There is no term like instantaneous work similar to instantaneous velocity.
Reason (R): For work to be done, the force must act for a displacement.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Velocity is a rate of change at an instant, but work \(W = \int F \cdot dr\) fundamentally involves displacement.
Instantaneous power \(P = F \cdot v\) exists, but not instantaneous work.
Reason (R) is true: Work requires a force to act over a non-zero displacement. Reason (R) correctly explains why instantaneous work is not a valid concept.
Assertion (A): A man of mass \(m\), standing on a frictionless surface pushes a wall and acquires a velocity \(v_0\). The work done by the wall on the man is non-zero.
Reason (R): Work done by all the forces is equal to change in kinetic energy.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: The wall exerts a reaction force on the man, which accelerates him to velocity \(v_0\). Since the man undergoes displacement while this force acts, the work done by the wall on the man is positive and non-zero, increasing his kinetic energy. Reason (R) is true: This is the Work-Energy Theorem (\(W_{net} = \Delta KE\)). Reason (R) correctly explains why the work done is non-zero as the man gains kinetic energy.
Assertion (A): Power delivered by all forces acting on a particle moving in a uniform circular motion is always zero.
Reason (R): Work done by all forces acting on a particle moving in a uniform circular motion is zero as KE remains constant.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: In uniform circular motion, the net force (centripetal force) is always perpendicular to the velocity. Power \(P = F \cdot v = |F||v| \cos 90^\circ = 0\). Reason (R) is true: Since speed is constant, kinetic energy \(KE\) is constant, thus \(Delta KE = 0\). By the Work-Energy Theorem, net work done \(W_{net} = \Delta KE = 0\). Reason (R) correctly explains why power is zero.