A body is projected vertically, upwards from earth's surface with velocity 2 V_e where V_e is the escape velocity from earth's surface. The velocity when body escapes the gravitational pull is

Step-by-step solution

To escape the gravitational pull F= G M m r^2 , the body needs to be at aligned & r & - ( G M m R )+ 1 2 m (V_e )^2=0 & V_e= 2 G M R aligned Therefore, if the particle is projected with 2 V_e from the surface of earth, then at r the velocity of the projectile is V . Considering energy conservation: aligned & - ( G M m R )+ 1 2 m (2 V_e )^2=0+ 1 2 m V^2 & - G M R + 1 2 (2 V_e )^2= 1 2 V^2 & - G M R + 4 G M R = 1 2 V^2 & V= 6 G M R = 3 ( 2 G M R )= 3 V_e aligned