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): 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): 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.
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
View Answer
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
View Answer
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): 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): 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
View Answer
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): 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
View Answer
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).