Question

Derive the expression fpr acceleration due to gravity

Answer 1

Acceleration due to gravity: The concept, expression and variations Expression for acceleration due to gravity At a Height 'h' From the Surface of the Earth: ... Let the acceleration due to gravity at this height be is 'gh'. Let 'r' be the distance of the body from the centre of the earth. If 'M' and 'R' are mass and radius of earth respectively then, r = R + h.

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.

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