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

$\frac{1}{2} \frac{G M m}{R}$
B

$\frac{1}{6} \frac{G M m}{R}$
C

$\frac{2}{3} \frac{G M m}{R}$
D

$\frac{1}{3} \frac{G M m}{R}$

Solution

Potential energy $U = \frac{- G M m}{r} = - \frac{G M m}{R + h}$
$U_{i n i t i a l} = - \frac{G M m}{3 R} a n d U_{f i n a l} = - \frac{- G M m}{2 R}$
Loss in PE = gain in $K E = \frac{G M m}{2 R} - \frac{G M m}{3 R} = \frac{G M m}{R} (\frac{1}{2} - \frac{1}{3}) = \frac{G M m}{R} (\frac{3 - 2}{6}) = \frac{G M m}{R} (\frac{1}{6})$

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