Find depth below Earth’s surface for reduced gravity

Practice question

Question

At what depth below Earth’s surface is g reduced to 8.33m/s2? (g0\=9.8m/s2,RE\=6.4×106m)

Options

Choose one · Correct answer highlighted

9.4 × 10⁵ m 9.6 × 10⁵ m Correct 9.8 × 10⁵ m 1.0 × 10⁶ m

Explanation

g(d) = g0(1−d/RE). 8.33 = 9.8(1−d/RE). 1−d/RE = 0.85. d/RE = 0.15. d = 0.15×6.4×106 = 9.6×105m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9.6 × 10⁵ m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

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