Gravitation

(a) Decreases - Acceleration due to gravity at depth h is given by $g_h$ = (1 – $\frac{2h}{R_e}$ )g, where $R_e=Radiusoftheearth,$ g = acceleration due to gravity on the surface of the Earth. From this equation, it is clear that acceleration due to gravity decreases with increase in height

(b) Decreases – Acceleration due to gravity at depth d is given by $g_d$ = (1- $\frac{d}{R_e}$ )g. So the acceleration due to gravity decreases with increase in depth.

(c) Mass of the body – Acceleration due to gravity of body mass m is given by the relation g = $\frac{GM}{R^2}$ , where G = Universal gravitation constant, M = mass of the Earth and R = radius of the Earth. Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.

(d) More – Gravitational potential energy of two points $r_1$ and $r_2$ distance away from the centre of the Earth is respectively given by:

V( $r_1$ ) = $-$ - $\frac{GmM}{r_1}$ and V( $r_2$ ) = $-$ - $\frac{GmM}{r_2}$

Difference in potential energy, V = V( $r_2$ ) $-$ V( $r_1$ ) = $-GmM(\frac{1}{r_2}$ $-\frac{1}{r_1}$ )

Hence this formula is more accurate than mg( $r_2$ - $r_1$ )