Question

A satellite of mass m is orbiting close to the surface of the earth (Radius R = 6400 km) has a K.E. K. The corresponding K.E. of satellite to escape from the earth’s gravitational field is 

(A) K 

(B) 2K 

(C) mg R 

(D) m K

Answer 1

Correct option: (B) 2K

Explanation:

Let V_o be orbital speed

hence

KE = (1/2) mV_o²                (1)

Let V_e be escape velocity

V_e = √2 ∙  V_o 

KE to escape field = (1/2)mV_e² 

KE' = (1/2)m × 2V_o²   

= mV_o²   

from (1), KE' = 2KE

given is KE = K hence KE' = 2K