The escape velocity v of a body depends on 1. the acceleration due to

1.	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» We know that, Escape velocity = V = [LT^-1 ] Acceleration due to gravity = g = [LT^-2] and Radius = R = [L] ⇒ Let V = kg^aR^b ⇒ [LT^-1] = [L^aT^-2a] [L^b] a + b = 1 and -2a = -1 ⇒ a = \(\frac {1}{2}\) and b =\(\frac {1}{2}\) So, V = k \(\sqrt {Rg.}\)

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»

We know that,

Escape velocity = V = [LT^-1 ]

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

and Radius = R = [L]

⇒ Let V = kg^aR^b

⇒ [LT^-1] = [L^aT^-2a] [L^b]

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

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

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

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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.

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