Practice question
Question
A moon orbits a planet with period 8 days and radius 3×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 8×86400 = 6.912×105s. T2 = 4.776×1011s2. r3 = (3×108)3 = 2.7×1025m3. M = 4×(3.14)2×2.7×10256.67×10−11×4.776×1011. M = 1.065×10263.185×101≈3.34×1024kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.4 × 10²⁴ kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
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