First slide

Gravitational potential and potential energy

Question

16kg and 9kg are separated by25m. The velocity with which a body should be projected from the midpoint of the line joining the two masses so that it just escape is

Moderate

A

$\sqrt{g}$
B

$\sqrt{2 g R}$
C

$\sqrt{G}$
D

$2 \sqrt{G}$

Solution

$P o t e n t i a l e n e r g y o f m a t m i d w a y d u e t o M_{1} a n d M_{2} = k i n e t i c e n e r g y \frac{- G M_{1} m}{\frac{d}{2}} + (\frac{- G M_{2} m}{\frac{d}{2}}) = \frac{1}{2} m v^{2} \frac{- 2 G (M_{1} + M_{2})}{d} = \frac{1}{2} v^{2} v = \sqrt{\frac{4 G (M_{1} + M_{2})}{d}} = \sqrt{\frac{4 G (16 + 9)}{25}} = 2 \sqrt{G}$

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