Question

A body enters in the gravitational field of the earth from external atmosphere.The potential energy of the earth body system

Answer 1

Given:

A body enters in the gravitational field of the earth from external atmosphere.

To find:

Potential energy of the earth body system ?

Calculation:

Let mass of body be m and mass of earth be M, radius of earth be r and height be h :

So, body enters gravitational field of earth from infinity and comes to lie at a height h from earth surface.

• So, the potential energy will be equal to the potential difference multiplied with the mass of the body.

$\therefore \: PE = \Delta V \times m$

$\implies\: PE = \bigg( V_{height} - V_{ \infty} \bigg ) \times m$

$\implies\: PE = \bigg \{ \dfrac{GM}{(r + h)} - \dfrac{GM}{ \infty} \bigg \} \times m$

$\implies\: PE = \bigg \{ \dfrac{GM}{(r + h)} - 0 \bigg \} \times m$

$\implies\: PE = \bigg \{ \dfrac{GM}{(r + h)} \bigg \} \times m$

$\implies\: PE = \dfrac{GMm}{(r + h)}$

So, final answer is:

$\boxed{ \bf\: PE = \dfrac{GMm}{(r + h)} }$