Derive an expression for the variation of acceleration due to gravity below the surface of the Earth.

Derive an expression for the variation of acceleration due to gravity

1.	Derive an expression for the variation of acceleration due to gravity below the surface of the Earth.
Answer» Solution :VARIATION of accleration due to gravity below the surface of earth : At a depth 'd' inside the ground mass of earth upto the point d from CETRE will exhibit force of attraction on the body. The remaining mass does not exhibit any influence. Mass of spherical body `M prop R^3` `:. M_s`/`M_E=(R_E-d)^3`/`R_E^3` where `M_S` is mass of earth's shell upto a depth 'd' from CENTRE. Gravitational force at depth 'd' is `F(d)=GM_s`m/`(R_E-d)^2=GM_Em(R_E-d)`/`R_E^2` `:.g(d)=(F(d))/(m)=(GM_E)/(R_E^3)(R_E-d)=g(R_E-d)=g(1-(d)/(R_E))` So 'g' VALUE decreases with depth below the ground.