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
\(\sqrt{(2GR^2}\)
B
\(\sqrt{(2GR)}\)
C
\(\sqrt{(2GM)}\)
D
\(\sqrt{(\frac{2G}{\text{R}})}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
v\(_e\) = \(\sqrt{(2gR)}\)
Since gR = GM
\(\therefore\), v\(_e\) = \(\sqrt{(2GM)}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #76386)