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
View Answer
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): Work done by conservative force along closed path is zero.
Reason (R): When an object is moved along closed path beginning and ending are at same point its displacement 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
View Answer
Assertion is true by definition of a conservative force, which does zero work over any closed path.
Reason is also true as displacement is zero for a closed path, i.e., \(\Delta \vec{r} = 0\). However, the reason is not the correct explanation for why work by a conservative force is zero; this is due to path independence and \(\Delta U = 0\) for a closed path.
Thus, both are true, but R is not the correct explanation of A.
Assertion (A): When a non-conservative force is involved in a system, it may dissipate energy.
Reason (R): The work done by a non-conservative force is always negative.
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 is true: Non-conservative forces like friction or air resistance dissipate mechanical energy into other forms (e.g., heat).
Reason is false: The work done by a non-conservative force is not always negative. For example, an applied external force can be non-conservative and do positive work on a system.
Thus, A is true but R is false.
Assertion (A): The sum of potential and kinetic energy for a system of moving objects is conserved only when no net external force acts on the objects
Reason (R): If no nonconservative force acts on a system of objects, the work done by external forces on a system of objects is equal to change in potential energy plus change in kinetic energy of the system.
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 is false: Mechanical energy \(E = K + U\) is conserved when only conservative forces do work. External conservative forces (e.g., gravity) can act and do work, yet mechanical energy can be conserved.
Reason is false: If no non-conservative forces act, then \(\Delta K + \Delta U = 0\), meaning mechanical energy is conserved. In this scenario, the work done by external forces \(W_{ext}\) is not necessarily zero. For instance, gravity does work when an object falls, but \(E\) is conserved.
Therefore, both Assertion and Reason 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
View Answer
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
View Answer
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
View Answer
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
View Answer
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
View Answer
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
View Answer
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.