Question

If a hole is made across the diameter of the earth and a boll is dropped from the surface into the hole. Then prove that the boll undergo the simple harmonic motion about the centre of earth.

Answer 1

F = m a = G M m / R^2    gravitational attraction

a = G M / R^2

M = 4/3 pi d R^3     mass of earth where d = density

a = 4/3 pi d G R = C1 R   (direction of increasing R opposite to a)

F = k x  (direction of increasing x opposite to F

F = m a    = k x    for SHM with spring

a = C2 x

both equations (earth and spring) have same form and same solution