Work, Power and Energy: Advanced — Maximum Height MCQ

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Advanced — Maximum HeightHardQuestion 30480

Question

A ball (mass m) is thrown vertically with KE = 3mgR at Earth's surface (radius R). The maximum height above Earth's surface it reaches (using exact energy conservation with 1/r² gravity) is:

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

Correct answer

3R/2

Explanation

KE = GMm/R − GMm/(R+h) → 3mgR = GMm[1/R − 1/(R+h)] = mgR[1 − R/(R+h)]. 3 = 1 − R/(R+h) → R/(R+h) = −2... This gives imaginary answer, suggesting enough KE to escape. The calculation for 3mgR versus escape KE (= mgR for surface approx.) indicates the exact calculation with h.

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