# What is Dimensional Formula of Escape velocity ?

Posted in Dimensional Formulae | Email This Post |Escape velocity is defined as minimum velocity required to escape from the gravitational pull of the earth.

Mathematically,

**Escape velocity (V _{e}) = ( 2 G M / r) ^{ 1/2}** where

G = Universal Gravitational constant

M = Mass of earth in kg

r= distance to center of earth in meters

Dimensional Formula of Universal Gravitational constant = M^{-1}L^{3}T^{-2}

Dimensional Formula of Mass of earth = M^{1}L^{0}T^{0}

Dimensional Formula of distance to center of earth = M^{0}L^{1}T^{0}

Putting these values in above equation we get,

**V _{e}** = ( [M

^{-1}L

^{3}T

^{-2}] [M

^{1}L

^{0}T

^{0}] / [M

^{0}L

^{1}T

^{0}] )

^{ 1/2}**V _{e}** = (M

^{0}L

^{2}T

^{-2})

^{ 1/2}

**V _{e}** = M

^{0}L

^{1}T

^{-1}

**Dimensional Formula of Escape velocity (V _{e}) = M^{0}L^{1}T^{-1}**

SI Unit of Escape velocity(V_{e}) is ms^{-1}

Escape velocity and orbital velocity of same dimension