The escape velocity v of a body depends on 1. the acceleration due to gravity ‘g’ and 2. the radius of planet ‘R’

Question

The escape velocity v of a body depends on

1. the acceleration due to gravity ‘g’ and

2. the radius of planet ‘R’

Find the relation between them using dimension analysis.

Answer 1

We know that,

Escape velocity = V = [LT-1 ]

Acceleration due to gravity = g = [LT-2]

and Radius = R = [L]

⇒ Let V = kgaRb

⇒ [LT-1] = [LaT-2a] [Lb]

a + b = 1 and -2a = -1

⇒ a = (\frac {1}{2}) and b =(\frac {1}{2})

So, V = k (\sqrt {Rg.})