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]

Options

A. `(1)/(2) (G M m)/( R)`
B. ` (1)/(6) (GM m)/(R)`
C. `(2)/(3) (G M m)/(R)`
D. `(1)/(3) (GM m)/(R)`

Answer

B

Explanation

When body starts falling to ward earth.s surface its potential energy decreases so kinetic energy increases. Increase in kinetic energy = Decrease in potential energy
Final kinetic energy - Initial kinetic energy = Initial potential energy - Final potential energy
Final kinetic energy ` - 0 = ((- GM m)/( r_(1))) - ((- GM m)/(r_(2))) = (-(GM m)/(R + h_(1))) - (- GM m )/( R + h_(2)))`
`= (- (GM m)/( R + 2R)) - (- (GM m)/( R + R)) = - (G M m)/( 3 R) + (G M m)/( 2 R) = (1)/(6) (G M m)/( R)`