Depth below Earth’s surface where gravity is 5.39 m/s²

Practice question

Question

At what depth below Earth’s surface is g reduced to 5.39m/s2? (g0\=9.8m/s2,RE\=6.4×106m)

Options

Choose one · Correct answer highlighted

2.8 × 10⁶ m 2.9 × 10⁶ m Correct 3.0 × 10⁶ m 3.1 × 10⁶ m

Explanation

g(d) = g0(1−d/RE). 5.39 = 9.8(1−d/RE). 1−d/RE = 0.55. d/RE = 0.45. d = 0.45×6.4×106 = 2.88×106m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.9 × 10⁶ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

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