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

Options

(a) Ve/√2
(b) Ve/2
(c) Ve/2√2
(d) Ve/4

Correct Answer:

Ve/2√2

Explanation:

Escape velocity of body from the earth’s surface is Ve=√2gR
Escape velocity of a same body at a height h from the earth’s surface is,Ve’=√2gR²/R+h
Given h=7R
Ve’=√2gR²/R+7R ⇒ √2gR²/R[1+7]
=√2gR/8 ⇒ 1/2√2 √2gR
=1/2√2 Ve.