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Question
How is acceleration due to gravity-related to
- mass of a planet
- distance of body from the center of the earth?
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Solution
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.
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