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]

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Solution

The correct option is B

When body starts falling towards earth's surface its potential energy decreases so kinetic energy increases.

Increases in Kinetic energy = Decrease in potential energy

Final kinetic energy - Initial kinetic energy = Initial potential energy - Final potential energy

Final kinetic energy - 0 = $(\frac{G M m}{r_{1}}) - (\frac{G M m}{r_{2}})$

$∴$ Final Kinetic energy = $(\frac{- G M m}{R + h_{1}}) - (\frac{G M m}{R + h_{2}})$

= $(\frac{G M m}{R + 2 R}) - (\frac{G M m}{R + R}) = - \frac{G M m}{3 R} + \frac{G M m}{2 R} = \frac{1}{6} \frac{G m M}{R}$ .

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