Question

mathematically Express the acceleration due to the gravity in terms of mass of the earth and radius of the earth

Answer 1

Hi there!

$F \: = \: m a \: \: \: \: \: \: \: \: \: \: \: - (1)$

$F \: = \: \frac{GMm}{ {r}^{2} } \: \: \: \: \: \: \: \: \: \: - (2)$

By -(1) and -(2)

$g \: = \: \frac{GM}{ {r}^{2} }$

Cheers!

Answer 2

Expression of acceleration due to gravity is given by:

• $g = \frac{GM}{R^2}$  
• Where,
• G is the gravitational constant(G = $6.67*10^{-11} Nm^2Kg^{-2}$  ), the value of G remains constant throughout the universe.
• R is the radius of the earth.
• M is the mass of the earth.
• g is the acceleration due to gravity.

What is acceleration due to gravity?

It is defined as acceleration exerted on any body due to the earth's gravitational force. It is only due to the earth's gravitational force and no other forces are involved.