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Question
A student says that he had applied a force \[F = - k\sqrt{x}\] 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.
Options
As x increases k increases.
As x increases k decreases.
As x increases k remains constant.
The motion cannot be simple harmonic.
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Solution
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:
F = -k\[\sqrt{x}\]...(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 \[\sqrt{x}\] .
Thus, as x increases k increases.
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