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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 the earth's surface. If the distance of the satellite from the earth's centre is increased by eight times its initial value, then the new angular momentum will be

Asked in JEE Main 8th April 2nd Shift 2023 · Angular momentum and elliptical orbits

• (1) 8L
• (2) 4L
• (3) 3L
• (4) 9L

Step-by-step solution

Why the other options are wrong

• (1) Scales L with the increase factor 8, which treats the angular momentum as proportional to r instead of to √r.
• (2) Reading the new radius as 8r instead of 9r gives √8=2.83, which rounds to 3, the key itself, so that route does not land here. No single consistent slip produces 4L; it is a filler distractor between 3L and 9L.
• (4) Uses the full radius ratio (9r)/r=9 as the answer and never takes the square root that L∝√r requires.

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