A body enters in the gravitational field of the earth from external at

1.	A body enters in the gravitational field of the earth from external atmosphere.The potential energy of the earth body system
Answer» en: 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: $\boxed{ \bf\: PE = \dfrac{GMm}{(r + h)} }$

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

Answer»

en:

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

Potential energy of the earth body system ?

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:

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