Practice question
Question
A moon orbits a planet with a period of 9 days and radius 6×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 9×86400 = 7.776×105s. T2 = 6.046×1011s2. r3 = (6×108)3 = 2.16×1026m3. M = 4×(3.14)2×2.16×10266.67×10−11×6.046×1011. M = 8.51×10264.033×101≈2.11×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.1 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.