What is Dimensional Formula of Escape velocity ?

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^-1L³T^-2
Dimensional Formula of Mass of earth = M¹L⁰T⁰
Dimensional Formula of distance to center of earth = M⁰L¹T⁰

Putting these values in above equation we get,

V_e = ( [M^-1L³T^-2] [M¹L⁰T⁰] / [M⁰L¹T⁰] ) ^1/2

V_e = (M⁰L²T^-2) ^1/2

V_e = M⁰L¹T^-1

Dimensional Formula of Escape velocity (V_e) = M⁰L¹T^-1
SI Unit of Escape velocity(V_e) is ms^-1