What is escape velocity? Obtain an expression for it.

Explanation

Escape speed `(V_1)_(min)`: It is defined as the minimum velocity required by a body to overcome gravitational field of earth is known as escape velocity.
For a body of mass 'm' gravitational potential energy on surface of earth `PE= -(G*m*M_E)/(R_E)`
For a body to escape from gravitational field of earth its kinetic energy must be equal or more than gravitational potential energy.
`KE=(1)/(2)mv^2` For minimum velocity KE=PE
`:. (1)/(2)mv^2= -(Gm*M_E)/(R_E)" or "v=sqrt((2GM_E)/(R_E))`
`:.` The minimum initial speed on surface of earth `(V_1)_(min)=sqrt((2GM_E)/(R_E))` is called esape speed, ( or) `V=sqrt(2gR_E)" " :.g=(GM)/(R^2)`.