Practice question
Question
A planet has a moon with an orbital radius of 5×108m and a period of 10 days. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
T2 = 4π2GMR3. M = 4π2R3GT2. T = 10×86400 = 8.64×105s. T2 = (8.64×105)2 = 7.465×1011s2. R3 = (5×108)3 = 1.25×1025m3. M = 4×(3.14)2×1.25×10256.67×10−11×7.465×1011. M = 4.93×10264.979×101≈9.9×1024kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.9 × 10²⁴ kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
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