⚛️ Physics · Gravitation · NEET & JEE

A body is dropped from rest at a height equal to the Earth radius R above the surface. Its speed on reaching the surface is about (g = 10 m/s², R = 6.4×10⁶ m):

Answer: 8 km/s.

A 8 km/s
B 2 km/s
C 4 km/s
D 11 km/s

Correct answer: A. 8 km/s

Explanation: Energy conservation: ½v² = GM(1/R - 1/2R) = gR/2, so v = √(gR) = √(6.4×10⁷) = 8000 m/s = 8 km/s.

g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.

Concept context

Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.

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A body is dropped from rest at a height equal to the Earth radius R above the surface. Its speed on reaching the surface is about (g = 10 m/s2, R = 6.4×106 m):

Concept context

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A body is dropped from rest at a height equal to the Earth radius R above the surface. Its speed on reaching the surface is about (g = 10 m/s², R = 6.4×10⁶ m):