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($\frac{1}{r_2}-\frac{1}{r_1}$) 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.

Answer 1

(a) decreases,
as we know, acceleration due to gravity at a height h from the earth's surface is given by, $g=\frac{g_0}{\left(1+\frac{h}{R}\right)^2}$
here it is clear that, if h increases , g will be decrease. Hence, Acceleration due to gravity decreases with increasing altitude.

(b) decreases,
acceleration due to gravity in depth h from the earth's surface is given by, $g=g_0\left(1-\frac{d}{R}\right)$
here it is clear that, if d increases , g will be decrease. Hence, Acceleration due to gravity decreases with increasing depth.

(c) mass of the body
Acceleration due to gravity is directly proportional to mass of planet and inversely proportional to square of separation between object and planet.
e.g., g = GM/R²
Hence, it is clear that , acceleration due to gravity is independent from mass of the body.

(d) GMm(1/r1 - 1/r2) is more accurate than the formula mg(r1 - r2). because GMm(1/r1 - 1/r2) is more suitable to use overall planets. but mg(r1 - r2) sounds like only for earth.

Answer 2

Answer:

(a) decreases,

as we know, acceleration due to gravity at a height h from the earth's surface is given by, g=\frac{g_0}{\left(1+\frac{h}{R}\right)^2}g=

(1+

R

h

)

2

g

0

here it is clear that, if h increases , g will be decrease. Hence, Acceleration due to gravity decreases with increasing altitude.

(b) decreases,

acceleration due to gravity in depth h from the earth's surface is given by, g=g_0\left(1-\frac{d}{R}\right)g=g

0

(1−

R

d

)

here it is clear that, if d increases , g will be decrease. Hence, Acceleration due to gravity decreases with increasing depth.

(c) mass of the body

Acceleration due to gravity is directly proportional to mass of planet and inversely proportional to square of separation between object and planet.

e.g., g = GM/R²

Hence, it is clear that , acceleration due to gravity is independent from mass of the body.

(d) GMm(1/r1 - 1/r2) is more accurate than the formula mg(r1 - r2). because GMm(1/r1 - 1/r2) is more suitable to use overall planets. but mg(r1 - r2) sounds like only for earth.