Minimum escape speed from 3 Earth radii

Practice question

Question

What is the minimum speed to escape from 3RE from Earth’s center? (g\=9.8m/s2,RE\=6.4×106m)

Options

Choose one · Correct answer highlighted

6.2 km/s 6.4 km/s 6.5 km/s Correct 6.7 km/s

Explanation

ve = 2gRE23RE = 2×9.8×6.4×1063. ve = 4.181×107≈6.47×103m/s≈6.5km/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.5 km/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

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