Page 66 - Force 10

Thus, equation (ii) becomes,

g’ = ( − ) …………..(iv)

Dividing equation (iv) by equation (ii)

′ −
=

Or, g’ = g −

∴ g’ = g − …………(v)

This relation shows that g’< g.

Thus the value of acceleration due to gravity decreases with depth. In other word, as we go

inside the earth, acceleration due to gravity goes on decreasing. At the centre of the earth, d =

R, hence equation (v) gives

g’ = 0

Consequently, the apparent weight of a body at the centre of the earth becomes zero.

i.e.. W = mg’ = m x 0 = 0
This gives weightlessness at the centre of the earth.