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 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 and $k$ remains constant
• D. the motion cannot be simple harmonic

Answer 1

Answer: (A)

It is given that $F=-k\sqrt{x}$
But For SHM $F=-k_{0}x$
Therefore by comparing them $k=k_{0}\sqrt{x}$
Therefore as $x$ increases $k$ increases