Question

Potential energy of a satellite having mass m and rotating at a height of 6.4 × 10⁶ m from the surface of earth 

(A) – 0.5 mg Re 

(B) – mg Re 

(C) – 2mgRe 

(D) 4 mgRe

Answer 1

Correct option: (A) – 0.5 mg Re

Explanation:

PE = [(– GMm) / r] = [(– GMm) / (Re + h)]

given h = 6.4 × 10⁶ = 6400 km

i.e.  h = Re

hence

PE = [(– GMm) / (2Re)]     also    V_e = √[(2GM) / Re] = √(2gRe)

i.e.      (GM / Re) = gRe

i.e.      GM = gRe² 

hence

PE = [(– gRe² ∙ m) / (2Re)]

PE = – 0.5 mg ∙ Re