⚛️ Physics · Gravitation · NEET & JEE

A body is projected vertically upward from Earth's surface with speed ve/2 (ve = escape speed). Max height reached:

Answer: R/3.

A R/3
B R/2
C R
D 2R

Correct answer: A. R/3

Explanation: Energy: (1/2)m(ve/2)2 - GMm/R = -GMm/(R+h). (ve2/8) - GM/R = -GM/(R+h). ve2 = 2gR = 2GM/R. GM/(4R) - GM/R = -GM/(R+h). -3GM/(4R) = -GM/(R+h). R+h = 4R/3. h = R/3.

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 projected vertically upward from Earth's surface with speed ve/2 (ve = escape speed). Max height reached:

Concept context

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