Question

Show the derivation of the value of 'g' (acceleration due to gravity).

Answer 1

F=ma

a towards the earth is is also termed as gravitational force

F=mg

F=Gmm/r^2

Also

F=mg

mg=Gm1m2/r^2

Cancel m both side

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.

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