Practice question
Question
A moon orbits a planet with a period of 7 days and radius 5×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 7×86400 = 6.048×105s. T2 = 3.658×1011s2. r3 = (5×108)3 = 1.25×1025m3. M = 4×(3.14)2×1.25×10256.67×10−11×3.658×1011. M = 4.93×10252.44×101≈2.02×1024kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.0 × 10²⁴ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
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