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(C) When a stone is dropped into a hole bored along the diameter of the earth,the gravitational force acting on the stone at a distance $r$ from the c

Vedclass · Accepted Answer

The stone executes simple harmonic motion about the centre of the earth.

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(C) When a stone is dropped into a hole bored along the diameter of the earth,the gravitational force acting on the stone at a distance $r$ from the centre is given by $F = -(\frac{GMm}{R^3})r$. Since the force is proportional to the displacement $r$ and directed towards the centre,the stone undergoes simple harmonic motion ($S$.$H$.$M$.) about the centre of the earth. The time period of this oscillation is given by $T = 2\pi \sqrt{\frac{R}{g}}$,where $R$ is the radius of the earth and $g$ is the acceleration due to gravity at the surface.

If a hole is bored along the diameter of the earth and a stone is dropped into the hole,what happens to the stone?

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