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).
Assertion (A): Work done by or against force of friction in moving a body in any round trip is always zero.
Reason (R): Frictional force is a conservative force.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Frictional force is a non-conservative force. Work done by a non-conservative force over a closed path is generally not zero. Therefore, both Assertion and Reason are false.
Assertion (A): No work is done when an electron completes a circular or an elliptical orbit around the stationary nucleus of an atom.
Reason (R): Electrostatic force is a conservative force.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Electrostatic force is a conservative force. For any conservative force, the work done on a particle moving along a closed path is zero. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of the Assertion.
Assertion (A): If a spring is compressed, energy is stored in spring and when it is elongated, energy is released.
Reason (R): Work done by spring force is equal to change in potential energy of the spring.
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
Elastic potential energy `\(U = \frac{1}{2} k x^2\)` is stored in a spring when it is compressed or elongated. Energy is released when the spring moves towards its equilibrium position, not during elongation itself. Thus, assertion (A) is false. For a conservative force like spring force, `\(W = -\Delta U\)`, so work done by spring force is equal to the negative of the change in potential energy.
Thus, reason (R) is also false. Both assertion and reason are false.