Practice question
Question
A satellite orbits a planet at 2.5×107m from its center with a period of 5 hours. What is the planet’s mass? (G\=6.67×10−11N m2/kg2)
Explanation
M = 4π2r3GT2. T = 5×3600 = 18000s, T2 = 3.24×108s2. r3 = (2.5×107)3 = 1.5625×1022m3. M = 4×(3.14)2×1.5625×10226.67×10−11×3.24×108. M = 6.158×10232.161×10−2≈2.85×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.9 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.