Practice question
Question
A satellite orbits a planet at 2×106m from its center with a period of 2 hours. What is the planet’s mass? (G\=6.67×10−11N m2/kg2)
Explanation
T2 = 4π2GMr3. M = 4π2r3GT2. T = 2×3600 = 7200s, T2 = 5.184×107s2. r3 = (2×106)3 = 8×1018m3. M = 4×(3.14)2×8×10186.67×10−11×5.184×107. M = 3.155×10203.458×10−3≈9.12×1022kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.1 × 10²² kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
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