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#gravitation numericals

2 public questions tagged with this topic.

Variation of g with Height and Depth

A satellite orbits a planet at 2×106m from its center with a period of 2 hours. What is the planet’s mass? (G\=6.67×10−1

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.

Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.

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Variation of g with Height and Depth

A 3kg mass is moved from 4RE to 8RE from Earth’s center. What is the change in potential energy? (ME\=6×1024kg,RE\=6.4×1

ΔV = −GMEm(1r2−1r1). r1 = 2.56×107m, r2 = 5.12×107m. ΔV = −6.67×10−11×6×1024×3(15.12×107−12.56×107). ΔV = −1.201×1015(−1.953×10−8)≈2.34×107J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.4 × 10⁷ J. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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