Define gravitational potential energy- Derive expression gravitational potential in the gravitational field of earth distance r from the centre of the earth- - - dfrac-2GMm-r- - - - dfrac-GMm-r- - - - dfrac-3GMm-r- - - - dfrac-4GMm-r-

Question

Toppr Admin · Accepted Answer

The work obtained in bringing a body from infinity to a point in gravitational field is called gravitational potential energy.

Force of attraction between the earth and the object when an object is at the distance $a$ from the center of the earth.

$F = \frac{G m M}{x^{2}}$

Consider the $d W$ is the small amount of work done in bringing the body without acceleration through the very small distance $d x$

$d W = F d x$

And total work done to bring the body from infinity to point $p$ which is at distance $r$ from the center of the earth.

$w = \int_{\infty}^{r} \frac{G m M}{x^{2}} d x = - \frac{G M m}{r}$

Hence, the gravitational potential energy $= - \frac{G M m}{r}$

Define gravitational potential energy. Derive expression for gravitational potential in the gravitational field of earth at distance r from the centre of the earth.=−2GMmr =−GMmr =−3GMmr =−4GMmr

Define gravitational potential energy. Derive expression for gravitational potential in the gravitational field of earth at distance $r$ from the centre of the earth.
$= - \frac{2 G M m}{r}$
$= - \frac{G M m}{r}$
$= - \frac{3 G M m}{r}$
$= - \frac{4 G M m}{r}$