An orbiting satellite has an orbital speed v = √(G M / r). If the orbital radius r is quadrupled, the new speed is
A{'text': 'v', 'label': 'A'}
B{'text': '2v', 'label': 'B'}
C{'text': 'v/2', 'label': 'C'}
D{'text': '4v', 'label': 'D'}
Answer & Solution
Correct answer: C. {'text': 'v/2', 'label': 'C'}
1. Orbital speed v = √(G M / r), so v ∝ 1/√r.
2. New r = 4r; new v = √(G M / 4r) = √(G M / r) / 2 = v/2.
3. Higher orbits have lower speeds but longer periods (Kepler's third law).
4. This is consistent with slower motion for outer planets like Neptune.
_Source: NCERT Class 11 Physics, Ch 7 "Gravitation", §7.6_
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