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.
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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Reason (R) is true as the weight returns to its starting point, making net displacement zero.
Assertion (A) is considered true in a physiological sense, as muscles expend energy. However, zero net displacement (R) implies zero net mechanical work on the weight by gravity, and thus zero net mechanical work by muscles if there is no change in kinetic energy. Therefore, (R) does not explain (A).
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
View Answer
Assertion (A) states the definition of a conservative force: the work done in a closed loop is zero.
Reason (R) states a key property of conservative forces: their work is path-independent. Path independence directly implies that the work done in any round trip (closed path) is zero, thus (R) correctly explains (A).
Assertion (A): A body cannot have kinetic energy without having linear momentum but it can have momentum without having mechanical energy.
Reason (R): Linear momentum and energy have same dimensions.
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 false:
If a body has linear momentum (\(p \neq 0\)), it must have velocity (\(v \neq 0\)), which implies it must also have kinetic energy (\(KE = \frac{1}{2}mv^2 \neq 0\)). Since kinetic energy is a component of mechanical energy, it cannot have momentum without mechanical energy.
Reason (R) is false: Linear momentum has dimensions \(MLT^{-1}\) while energy has dimensions \(ML^2T^{-2}\), which are different.
Assertion (A): A spring has potential energy, both when it is compressed or elongated.
Reason (R): In compressing or stretching, work is done on the spring against the restoring force.
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:
A spring stores elastic potential energy, calculated as \(U = \frac{1}{2}kx^2\), when it is compressed or stretched from its equilibrium position.
Reason (R) is true: This potential energy is stored because an external force does work against the spring's restoring force during deformation. Reason (R) correctly explains Assertion (A).
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.