JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Gravitation

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Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be:

(A)Potential energy
(B)Total energy
(C)Kinetic energy
(D)Speed✓ Correct

Answer: (D)

Solution

For a satellite in orbit, the orbital speed is given by

v = \frac{G M _{P}}{R}

, where

M_{P}

is the mass of the planet and

R

is the orbital radius. This expression is independent of the satellite's mass. However, potential energy

P E = - \frac{G M _{P} M}{R}

, kinetic energy

K E = \frac{G M _{P} M}{2 R}

, and total energy

T E = - \frac{G M _{P} M}{2 R}

all depend on the satellite's mass

M

. Since both satellites are in the same orbit (same

R

), they have the same speed.

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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