An exam solution gives the escape velocity from the surface of a planet as v_ e = 2 G…

PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

An exam solution gives the escape velocity from the surface of a planet as

v_{e} = \sqrt{\dfrac{2 G M}{R^{3}}},

where

G

is the gravitational constant,

M

the mass of the planet and

R

its radius. Use dimensional analysis to write the corrected form of this formula, retaining only one numerical constant.