Matching Satellite Energies – Rankers Physics
Topic: Gravitation
Subtopic: Planet and Satellite

Matching Satellite Energies

For energy of satellite, match the columns (symbols have their respective meaning): **Column-I** (i) Kinetic energy (ii) Potential energy (iii) Total energy **Column-II** (p) \(\frac{L^2}{2mr^2}\) (q) \(-\frac{L^2}{mr^2}\) (r) \(-\frac{L^2}{2mr^2}\)
(1) i-q ; ii-p ; iii-r
(2) i-p ; ii-r ; iii-q
(3) i-p ; ii-q ; iii-r
(4) i-r ; ii-q ; iii-p

Solution:

Kinetic energy \(K = \frac{1}{2}mv^2 = \frac{L^2}{2mr^2}\) (since \(L = mvr\)). Potential energy \(U = -\frac{GMm}{r} = -\frac{L^2}{mr^2}\). Total energy \(E = K + U = -\frac{L^2}{2mr^2}\). Thus (i)-p, (ii)-q, (iii)-r.

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