Question

if a ball is made along the diameter of earth and an iron ball is dropped from one end of the bore, how the bar will behave in the bore?​

Answer 1

If a ball is dropped in the bore passing through earth's center then it will execute a simple harmonic motion and keep going in back and forth motion.

Reason :

The force of attraction is given by,

F = Gm₁m₂/r²

where m₁ = mass of earth = ρV = ρ x (4/3) x πr³

hence the force is given by,

F = G x ρ x (4/3) x πr³ m₂/r² = kr

where k is a constant,

F ∝ r

If the force acting on a body is directly proportional to the displacement and acts opposite to the direction of motion, the body executes Simple Harmonic Motion.