Practice question
Question
A moon orbits a planet with a period of 13 days and radius 1.0×109m. What is the planet’s mass? (G\=6.67×10−11N m2/kg2,1day\=86400s)
Explanation
M = 4π2r3GT2. T = 13×86400 = 1.1232×106s. T2 = 1.262×1012s2. r3 = (1.0×109)3 = 1.0×1027m3. M = 4×(3.14)2×10276.67×10−11×1.262×1012. M = 3.947×10278.418×101≈4.69×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.7 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.