Question

Derivation of acceleration due to gravity in terms of radius and mass of Earth

Answer 1

Answer:

Formula of Acceleration due to Gravity

G = universal gravitational constant (6.67×10-11 Nm2/kg2) m = mass of the object, M = mass of the earth, r = radius of the earth.

Formula: g = GM/r2

Dimensional Formula: M0L1T-2

SI Unit: ms-2

Values of g in SI: 9.806 ms-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.

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