Question

Derive the formula to calculate acceleration due to gravity.

Answer 1

g = GM/R^2

g= 6.7×10^-11×6×10^24/(6×10^6)^2

g=.6.7×6×10^14/6×10^6)^2

g= 9.8

mathematical derivation for acceleration due to gravity

F = ma

where m is mass. and a is acceleration

Gravitational force acting on mass on earth surface

G= Mm/R^2 = ,m=GM/R^2

where G is gravitational force of earth , M is a mass , R is radius

by comparing two equation

g= GM/R^2

Answer 2

Answer :-

According to the gravitational law

$\sf F = \frac{GMm}{R^2}$ - i

According to Newton's second law of motion -

F = ma - ii

From equation i and ii :-

$\sf ma = \frac{GMm}{R^2}$

$\sf a = \frac{GM}{R^2}$

This a is known as acceleration due to gravity.

$\boxed{\sf a = g = \frac{GM}{R^2}}$