A body of mass m kg. starts falling from a point 2R above the earth's surface. Its kinetic energy when it he
fallen to a point 'R'above the earth's surface [R-Radius of earth, M-Mass of earth, G-Gravitational constar

Options

A. `(1)/(2)("GMm")/(R)`
B. `(1)/(6)("GMm")/(R)`
C. `(2)/(3)("GMm")/(R)`
D. `(1)/(3)("GMm")/(R)`

Answer

B

Explanation

When body starts falling toward earth.s surface its potential energy decreases so kinetic energy incresases
Increase in kinetic energy= Decrease in potential energy
Final kinetic energy- Initial kinetic energy = Initial potential energy - Final potential energy
Final kinetic energy-0= `((-"GMm")/(r_(1)))-((-"GMm")/(r_(2)))=(-("GMm")/(R+h_(1))) -((-"GMm")/(R+h_(2)))`
`=(-("GMm")/(R+2R))-(-("GMm")/(R+R))=-("GMm")/(3R)` `+("GMm")/(2R)=(1)/(6)("GMm")/(R)`