Question

How is acceleration due to gravity-related to

1. mass of a planet
2. distance of body from the center of the earth?

Answer 1

Acceleration due to gravity: The acceleration of a freely falling body, under the action of gravity of earth, is called acceleration due to gravity.
Consider a body of mass ‘m’ on the surface of the earth such that it falls towards it with an acceleration ‘g’.
Let, M = mass of the earth
d = distance between center of earth and center of the body
F = Force acting on the body
F = mg .............(i)

F = `"G""Mm"/"d"^2` ...............(ii)

Comparing (i) and (ii)

mg = `"G""Mm"/"d"^2`

g = `"Gm"/"d"^2`

From this equation, it is clear that

1. g α M
Acceleration due to gravity on the earth is directly proportional to the mass of that earth.

2. g α `1/"d"^2`
Acceleration due to gravity is inversely proportional to the square of the distance of the body from centre of the earth.