First slide

Gravitational potential and potential energy

Question

A body of mass m kg starts falling from a point 2R above the Earth's surface. Its kinetic energy when it has fallen to a point R above the Earth's surface [R: Radius of Earth, M:Mass of Earth, G: Gravitational Constant]

Moderate

A

$\frac{1}{2} \frac{GMm}{R}$
B

$\frac{1}{6} \frac{GMm}{R}$
C

$\frac{2}{3} \frac{GMm}{R}$
D

$\frac{1}{3} \frac{GMm}{R}$

Solution

$Potential energy, U = \frac{- GMm}{r} = - \frac{GMm}{R + h}$
$\begin{array}{l} U_{initial} = - \frac{GMm}{3 R} and U_{final} = - \frac{- GMm}{2 R} \\ Loss in PE = gain in KE = \frac{GMm}{2 R} - \frac{GMm}{3 R} = \frac{GMm}{6 R} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App