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Simple Harmonic Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSimple Harmonic Motion1 Mark
MCQ
A student says that he had applied a force $\text{F}=-\text{k}\sqrt{\text{x}}$ on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.
  • ✓
    As x increases k increases.
  • B
    As x increases k decreases.
  • C
    As x increases k remains constant.
  • D
    The motion cannot be simple harmonic.
✓

Answer

Correct option: A.
As x increases k increases.
A body is said to be in simple harmonic motion only when,
F = -kx .....(1)
where F is force,
k is force constant, and,
x is displacement of the body from the mean position.
Given:
$\text{F}=-\text{k}\sqrt{\text{x}}\ ...(2)$
On comparing the equations (1) and (2), it can be said that in order to execute simple harmonic motion, k should be proportional to $\sqrt{\text{x}}$ Thus, as x increases k increases.

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