A body of mass m kg starts falling from a point 2R above the earth's surface. Its kinetic energy when its 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(GMm)/R`
B. `1/6(GMm)/R`
C. `2/3(GMm)/R`
D. `1/3(GMm)/R`

Answer

B

Explanation

Potential energy `U=-(GMm)/r=-(GMm)/(R+h)`
`U_("initial")=-(GMm)/(3R)` and `U_("final")=-(-GMm)/(2R)`
Loss in PE=gain in KE `=(GMm)/(2R)-(GMm)/(3R)=(GMm)/(6R)`