Work Done Against Gravity - Practice Questions & MCQ

The gravitational potential energy at height 'h' from the earth's surface

$
U_h=-\frac{m g R}{1+\frac{h}{R}}
$

So at the surface of earth put $h=0$
We get $U_s=-m g R$
So if the body of mass $m$ is moved from the surface of earth to a point at height $h$ from the earth's surface Then there is a change in its potential energy.

And this change in its potential energy is known as work done against gravity to move the body from earth surface to height $h$.

$
W=\Delta U=G M m\left[\frac{1}{r_1}-\frac{1}{r_2}\right]
$

Where $W \rightarrow$ work done
$\Delta U \rightarrow$ change in Potential energy
$r_1, r_2 \rightarrow$ distances

Putting $r_1=R$, and $r_2=R+h$

$
W=\Delta U=G M m\left[\frac{1}{R}-\frac{1}{R+h}\right]
$

1. when ' $h$ ' is not negligible

$
W=\frac{m g h}{1+\frac{h}{R}}
$
 

2.  when ' $h$ ' is very small

   $
   W=\frac{m g h}{1+\frac{h}{R}}
   $

   
   But $h$ is small as compared to earth's radius

   $
   \frac{h}{R} \rightarrow 0
   $

   so $W=m g h$
   3. If $h=n R$ then

   $
   W=m g R * \frac{n}{n+1}
   $