Question

find the minimum velocity to be imparted to a body so that it escapes from solar system

Answer 1

Its kinetic energy must exceed the potential energy due to gravitation from the sun,

(1/2) m v^2 > G m M / r

where G is universal gravitation constant, m and M are its mass and solar mass and r is how far from the sun it starts.

Answer 2

to escapes from Earth
k.e energies should exceed the total energy
(1/2) m v^2 > ke + pe
now pe = -gmM/r (r= radius of earth + height above the surface of earth )
ke= (1/2) m v^2
but v^2 =gm/r (r= radius of earth + height above the surface of earth )
KE = 1/2gmM/r
therefore T .E > ke+ pe
T .E > -gmM/2r (r= radius of earth + height above the surface of earth )
(1/2) m v^2 > -gmM/2r (r= radius of earth + height above the surface of earth )

Answer 3

The escape velocity needed will depend on where the object starts and which gravitational field / potential is dominant. I assumed "Sun" from "solar system," but perhaps "Earth" is what is wanted. Thus, mass of earth and distance from it or mass of sun and distance from it would prevail.