Question

The escape velocity of a body from earth’ surface is Ve. The escape velocity of the same body from a height equal to 7 R from earth’ surface will be

(A) (Ve / √2)

(B) (Ve / 2)

(C) (Ve / 2√2)

(D) (Ve / 4)

Answer 1

Correct option: (C) (Ve / 2√2)

Explanation:

V(e)1 = earths escape velocity = √[(2GM) / R] (1)

V(e)2 = escape velocity from height h = √[(2GM) / (R + h)]

= √[(2GM) / (R + 7R)]------ h = 7R (2)

V(e)2 = √[(2GM) / (8R)]

from (1) & (2)

(V(e)2 / V(e)1) = √(1/8)

V(e)1 = √8 V(e)2

V(e)2 = (V(e)1 / √8) = (V(e)1 / 2√2)