Practice question
Question
A moon orbits a planet with a period of 12 days and radius 9×108m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 12×86400 = 1.0368×106s. T2 = 1.075×1012s2. r3 = (9×108)3 = 7.29×1026m3. M = 4×(3.14)2×7.29×10266.67×10−11×1.075×1012. M = 2.875×10277.171×101≈4.01×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.0 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.