Question

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.

(a) U < K .

(b) U > K.

(c) U = K.

Answer 1

(b ) ​U>K.

EXPLANATION: 

Let the mass of the moon = m, velocity v and its distance from the earth = a.  

v = √(GM/a), K.E. = K = ½mv² = ½m*GM/a 

→GMm/a = 2K 

The magnitude of gravitational potential energy of the moon  

U = GMm/a =2K 

Obviously U>K.