Question

A student says that he had applied a force F = -k/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 has worked only with positive x and no other force acted on the particle.
(a) 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 1

Answer ⇒ Option (a). As x increases k increases.

Explanation ⇒ As already mentioned in the question, the  motion of the Particle is Simple Harmonic Motion.

∴ Force = -mω²x

Now, As the force which the students mentioned = -k/x

If the motion is S.H.M., then both will be equal.

∴ -k/x = -mω²x

∴ k = mω²x²,

this means if x increases then k also increases.

Therefore, Option (a) is correct.

Hope it helps.

Answer 2

Answer: (a)

Explanation: It's not known whether k is a constant or not, but it's known that the particle moved in simple harmonic motion.

So, -k×1/√x×x= F or k^1/√x is a constant.

Thus k is proportional to √x.

So if x increases, k will increase as well.