Answer :
Answer:
d) Rate of change of angular momentum
Explanation:
To determine which quantity is zero if the torque on a particle is zero, we need to understand the relationship between torque and these physical quantities.
Understanding Torque and Angular Momentum:
Torque (τ) is related to the rate of change of angular momentum (L) by the equation:
[tex]\tau = \dfrac{dL}{dt}[/tex]
If the torque on a particle is zero (τ = 0), then the rate of change of angular momentum is also zero:
[tex]\dfrac{dL}{dt}=0[/tex]
This means that the angular momentum 'L' of the particle is constant over time.
Analyzing the Options:
- (a) Angular momentum of the particle: If the torque is zero, the angular momentum is constant, but not necessarily zero.
- (b) Angular speed of the particle: The angular speed could remain constant or change depending on other forces acting on the particle, so this is not necessarily zero.
- (c) Change in kinetic energy of the particle: Kinetic energy change is related to work done, which depends on forces, not directly on torque.
- (d) Rate of change of angular momentum: As derived above, if torque is zero, the rate of change of angular momentum is zero.
The correct answer is (d) Rate of change of angular momentum. If the torque on a particle is zero, the rate of change of angular momentum must also be zero.