Choose the correct alternative
(a)Acceleration due to gravity increase/decrease with increasing altitude.
(b) Acceleration due to gravity increase/decrease with increasing depth (assume the earth to be a sphere of uniform density).
(c ) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula `- GM m ((1)/(r_(2)) - (1)/(r_(1)))` is more/less accurate than the formula `mg (r_(2) - r_(1))` for the difference of potential energy between two points `r_(2)` and `r_(1)` distance away from the centre of earth.

Options

A. Acceleration due to gravity increases/decreases with increasing altitude.
B. Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density.)
C. Acceleration due to gravity is independent of the mass of the earth/mass of the body.
D. The formula – GMm `(1/r_2-1/r_1)` is more/less accurate than the formula mg `(r_2 – r_1)` for the difference of potential energy between two points `r_2` and `r_1` distance away from the centre of the earth.

Explanation

Acceleration due to gravity at altitude h from the earth's surface is given by `g'=g/((1+h/R_e)^2)`
Where `R_e` is the radius of the earth.
Therefore, acceleration due to gravity decreases with increasing altitude.
(ii) Acceleration due to gravity at depth h from the earth's surface is given by `g'=g(1-h/R_e)`
Therefore, acceleration due to gravity decreases with increasing depth.
(iii) Acceleration due to gravity is independent of the mass of the body.
The formula `-GMm(1/r_2-1/r_1)` is more accurate than the formula mg `(r_2 – r_1)` for the difference potential energy between two points `r_2` and `r_1` distance away from the centre of the earth.