Question

Why does the weight of a body of a finite mass m is zero at the centre of the Earth?

Answer 1

Acceleration at depth d due to gravity is given by,

g_d = g\((1-\frac{d}{R})\)

As, at centre of the Earth d = R ⇒ g_d = 0.

Hence, the weight of a body of a finite mass m is zero at the centre of the Earth.