Question

What is meant by acceleration due to gravity ? Derive an expressing for acceleration
due to gravity in terms of earth and its radius R.

​

Answer 1

Here's ur answer...

The acceleration which is gained by an object because of the gravitational force is called its acceleration due to gravity. Its SI unit is m/s2 . Acceleration due to gravity is a vector, which means it has both a magnitude and a direction.

Derivation....

From the Newton’s Second Law of Motion, we can write

F=ma

Here, F is the force acting on the object, m is its mass and ‘a’ is the acceleration.

Also, as per Newton’s Law of Gravity, we can write,

Fg=GMm(r+h)2

It is the gravitational force acting between two bodies lying in the gravitational field of each other. This force acts inwards and is attractive in nature. Each of the two bodies experience the same force directed towards the other.

Using the Newton’s second law of motion, in order to find the acceleration of the body under this condition,

a=Fgm

Here, m is the mass of the object for which the acceleration due to gravity is to be calculated.

a=g=GMm(y+h)2m

g=GM(y+h)2

Also, when the object is on or near to the surface the value of g becomes constant and does not change considerably with the height. Hence, we can write,

g=gMr2