The magnitude of gravitational potential energy of the moon earth system is U with zero potential energy at infinite separation. The kinetic energy of the moon with respect to the earth is K.

Options

A. |U| = K
B. |U| `lt ` K
C. |U| `gt` K
D. either B or C

Answer

C

Explanation

The orbital velocity of moon is
`v_(0m) = sqrt((GM_(e))/(r)) " "`............(i)
So kinetic energy of moon is K= 1/2 `M_(m) v_(om)^(2)`
`(GM_(e)M_(m))/(2r) " "`.............(ii)
`U = - (GM_(e)M_(m))/(r)" "`.............. (iii)
where r is distance between the centres of earth & moon.
It is clear from (ii) & (iii) that U`gt`K (in magnitudes term)