Q151 / 200 · MHT CET - Medical 2026 (21 April Shift 1) · Physics
For a particle executing simple harmonic motion , which of the following statements is NOT correct?
- AThe magnitude of acceleration is directly proportional to displacement.
- BThe restoring force is always directed towards fixed point.
- CThe restoring force is maximum at extreme position.
- Correct answerDThe acceleration of the particle is maximum at equilibrium position.
Solution
In simple harmonic motion, the acceleration of a particle is given by $a = -\omega^2 x$, where $x$ is the displacement from the equilibrium position.
At the equilibrium position, the displacement $x = 0$.
Substituting $x = 0$ in the expression for acceleration, we get $a = 0$.
Thus, the acceleration of the particle is minimum (zero) at the equilibrium position, not maximum.
The restoring force $F = -kx$ is directed towards the equilibrium position and its magnitude is maximum at the extreme positions where $x = \pm A$.
Therefore, the statement that acceleration is maximum at the equilibrium position is incorrect.
Answer: The acceleration of the particle is maximum at equilibrium position.
At the equilibrium position, the displacement $x = 0$.
Substituting $x = 0$ in the expression for acceleration, we get $a = 0$.
Thus, the acceleration of the particle is minimum (zero) at the equilibrium position, not maximum.
The restoring force $F = -kx$ is directed towards the equilibrium position and its magnitude is maximum at the extreme positions where $x = \pm A$.
Therefore, the statement that acceleration is maximum at the equilibrium position is incorrect.
Answer: The acceleration of the particle is maximum at equilibrium position.
Hence, the correct answer is option: 'D'.