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): Total energy is negative for a bounded system.
Reason (R): Potential energy of a bound system is negative and its magnitude is more than 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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For a bound system, the potential energy (\(U\)) is negative and its magnitude is greater than the kinetic energy (\(K\)). Since total energy is \(E = K + U\), \(E\) must be negative. Both Assertion and Reason are true, and Reason correctly explains Assertion.
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): The work done by a non-conservative force is always negative.
Reason (R): When a non-conservative force is involved in a system, it always dissipates 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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Work done by non-conservative forces can be positive (e.g., applied force) or negative (e.g., friction), so (A) is false.
Non-conservative forces can dissipate (friction) or add (engine thrust) energy. So (R) is also false.
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): Two balls of different masses are thrown vertically upwards with same speed. They will pass through their point of projection in the downward direction with the same speed in absence of air resistance.
Reason (R): In absence of air resistance, the mechanical energy of a projectile is conserved.
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 the absence of air resistance, only gravity acts, a conservative force. Thus, mechanical energy is conserved. This implies that the speed at any height (including projection point) is the same, irrespective of mass.
Both Assertion and Reason are true, and Reason correctly explains Assertion.
Assertion (A): If in a round trip work done by a force is zero then force is conservative.
Reason (R): Work done by conservative force field is independent of path.
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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A conservative force is defined by two equivalent properties: work done in a closed loop is \(0\) and work done is path-independent. If \(W_{\text{round_trip}} = 0\), the force is conservative. \(W_{\text{conservative}} = 0\) for a round trip because it is path-independent, meaning \(W_{A to B} = -W_{B to A}\). Thus, Reason (R) correctly explains Assertion (A).
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.