JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Gravitation

A satellite is revolving in a circular orbit at a height h from the earth surface, such that

h ≪ R

where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:

(A) $2 gR$
(B) $gR$
(C) $\frac{gR}{2}$
(D) $gR (2 - 1)$ ✓ Correct

Answer: (D)

Solution

In the low orbit, where

h ≪ R

, the satellite already moves at the orbital speed

v_{o} = GM / R

, and to break free it must reach the escape speed

v_{e} = 2 GM / R

from that radius. The extra speed it must be given is the difference

Δ v = v_{e} - v_{o} = GM / R (2 - 1)

. Writing

GM / R = g R

through

g = GM / R^{2}

, this becomes

g R (2 - 1)

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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