Practice question
Question
A moon orbits a planet with a period of 11 days and radius 8×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 11×86400 = 9.504×105s. T2 = 9.028×1011s2. r3 = (8×108)3 = 5.12×1026m3. M = 4×(3.14)2×5.12×10266.67×10−11×9.028×1011. M = 2.019×10276.022×101≈3.35×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.4 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
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