BITSAT 2022 Paper

Acceleration due to gravity at the surface of earth,
g=G

M

R2

=

4

3

πρGR.................(i)
[∵M=

4

3

πR3.ρ]
Where, ρ= density of earth.
Acceleration due to gravity at depth d from the surface of earth,
g′=

4

3

πρG(R−d)...........(ii)
From Eqs. (i) and (ii), we get
g′=g[1−

d

R

]