Question

If ‘V’ is velocity and ‘a’ is acceleration of a particle executing linear simple harmonic motion. Which one of the following statements is correct?

• A. when ‘a’ is maximum, v is maximum
• B. when ‘a’ is maximum, v is zero
• C. when ‘a’ is zero, v is zero.
• D. ‘a’ is zero for any value of ‘v’

Answer 1

The Correct Option is C

In linear simple harmonic motion, the acceleration and velocity of the particle are related to each other. 
The acceleration is maximum when the particle is at the extreme positions (maximum displacement) of the oscillation. At these points, the velocity is momentarily zero, as the particle changes direction.
when the acceleration is zero, the particle is at the equilibrium position (midpoint) of the oscillation, and at this point, the velocity is also zero.
Therefore, when 'a' is zero, 'v' is zero.

Answer 2

In linear simple harmonic motion (SHM):

Acceleration a is maximum at the extremes of displacement (maximum amplitude), where the particle changes direction.
Velocity v is zero at these extremes because the particle momentarily stops before changing direction.
Acceleration is zero at the equilibrium position (midpoint) of the oscillation, where the restoring force is zero.
Velocity is also zero at the equilibrium position because the particle momentarily stops before reversing its direction of motion.

Therefore, the statement "when 'a' is zero, 'v' is zero" accurately describes the relationship between acceleration and velocity in linear SHM.

So, the correct option is (C): When 'a' is zero, 'v' is zero.