A satellite of mass m is orbiting a planet of mass M at a radial distance r 0 from the centre of the planet. The satellite expels a small mass in a direction opposite to its orbital velocity. The im

Question

A satellite of mass m is orbiting a planet of mass M at a radial distance $r_{0}$ from the centre of the planet. The satellite expels a small mass in a direction opposite to its orbital velocity. The immediate recoil velocity of the satellite exceeds the initial orbital velocity by $Δ v$ . The largest possible value of $Δ v$ for which the satellite remains within the gravitational field of the planet is

Options:

Answer:

C

Solution:

$v_{e} = 2 \frac{GM}{r _{0}}$

$∴ Δ v = v_{e} - v_{0} = (2 - 1) \frac{GM}{r _{0}}$

TestHub · Accepted Answer

v e ​ = 2 ​ r 0 ​ GM ​ ​ ∴ Δ v = v e ​ − v 0 ​ = ( 2 ​ − 1 ) r 0 ​ GM ​ ​

Physics - Electrostatics Question with Solution | TestHub

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JEE Advanced (2028)