What is the escape velocity of a body on the surface of the earth of radius R if the gravitational constant is G and the mass of the earth is M? (Neglect energy losses to the surroundings)
A
2GR
B
2G/R
C
2GR2
D
\(\sqrt{\frac{2GM}{R}}\)
Verified Correct Answer: D.
Physical Principles & Numerical Solution
Set initial total energy to zero:
\(\frac{1}{2}mv^2 - \frac{GMm}{R} = 0\)
\(\frac{1}{2}mv^2 = \frac{GMm}{R}\)
\(v^2 = \frac{2GM}{R}\)
\(v = \sqrt{\frac{2GM}{R}}\)
Source: Myschool Past Questions Archive (Record #25087)