Question

A satellite with K.E. E_k is revolving round the earth in a circular orbit. How much more K.E. should be given to it so that it may just escape into outer space ? 

(A) E_k 

(B) 2 E_k 

(C) (1/2)E_k 

(D) 3 E_k

Answer 1

Correct option: (A) E_k

Explanation:

Let V_o be orbital speed.

hence E_k = (1/2)mV₀² 

Let V_e be escape velocity

then V_e = √2 V_o 

KE required for rscape = E_k'

hence  E_k' = (1/2)mV_e² 

= (1/2) × m × 2V_o² 

E_k' = mV_o² 

i.e. E_k' = 2E_k 

hence

additional KE = 2E_k – E_k = E_k