Question

define acceleration due to gravity . Derive an expressions for acceleration due to gravity at the surface of the earth​

Answer 1

Answer:

1) Define acceleration due to gravity .

The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation and the centrifugal force. In SI units this acceleration is measured in metres per second squared or equivalently in newtons per kilogram.

2) Derive an expressions for acceleration due to gravity at the surface of the earth.

Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.

Answer 2

Answer :-

The acceleration produced in a body falling free under gravitational pull of earth is called acceleration due to gravity.

Derivation :-

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.

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