JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Rotational Mechanics

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The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be-

(A)8 L
(B)4 L
(C)9 L
(D)3 L✓ Correct

Answer: (D)

Solution

The orbital angular momentum is

L = m v r

. For a satellite in circular orbit,

v = \frac{G M _{e}}{r}

, so

L = m \frac{G M _{e}}{r} \cdot r = m G M_{e} r

. Thus

L \propto r

. If the distance from the center increases by 8 times (from r to r + 8r = 9r), the new angular momentum is

L^{'} \propto 9 r = 3 r

. Therefore

\frac{L ^{'}}{L} = \frac{3 r}{r} = 3

, giving

L^{'} = 3 L

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Single correct option

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