Practice question
Question
A moon orbits a planet with a period of 10 days and radius 7×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 10×86400 = 8.64×105s. T2 = 7.465×1011s2. r3 = (7×108)3 = 3.43×1026m3. M = 4×(3.14)2×3.43×10266.67×10−11×7.465×1011. M = 1.353×10274.979×101≈2.72×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.7 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.