define escape velocity .derive expression for it
The minimum velocity with which a projectile has to be projected to escape the earth’s gravitational field is called escape velocity.
Let a body of mass ‘m’ be projected with velocity ‘v’.
At the ground, PE = GMm/R
And the KE = ½ mv2
To overcome earth’s gravitational field,
=> ½ mv2 > GMm/R
=> v > (2GM/R)1/2
g = GM/R2
v > [2(GM/R2)R]1/2
=> v > [2gR]1/2
Thus, to escape the earth’s gravitational field, the minimum velocity must be,
ve = [2gR]1/2