Question

Choose the correct alternative :
(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 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 center of the earth.

Answer 1

(a) Acceleration decreases according to formula $g^{\prime }=g(1-\frac{2h}{R})$,
where h is height and R is radius of earth.

(b) Acceleration decreases according to formula $g^{\prime }=g(1-\frac{d}{R})$,

where d is depth and R is radius of earth.

(c) Acceleration due to gravity is given by the formula: $g=\frac{G{M}_e}{R_e^2}$

Hence, it is independent of mass of body, but is dependent on mass of earth.

(d) Gravitational potential energy is given by the formula: $U=-\frac{G{m}_1{m}_2}{r}$

$g=\frac{G{M}_e}{R_e^2}$ assuming distance between object and earth is nearly equal to the radius of the earth.

Substituting the second equation in first, we get $U\approx mgh$

Hence, the first formula is more accurate.