A body is projected vertically upwards from earth's surface of radius ' R ' with velocity equal to 1 3 of escape velocity. The maximum height reached by the body is

Step-by-step solution

K.E. = U Let mass of the particle be M and that of the Earth be M _ e 1 2 Mv ^2= GM _ e M ( 1 R - 1 R + h ) Also, g = GM _e R ^2 Equation (i) can be written as, array ll & 1 2 v ^2= GM _ e [ R + h - R R ( R + h ) ]= GM _ e R ^2 [ Rh ( R + h ) ] & 1 2 ( 1 3 v _ e )^2= gRh R + h & 1 2 ( 1 3 2 gR )^2= gRh R + h & 1 2 1 9 (2 gR )= gRh R + h & h R + h = 1 9 & 9 ~h = R + h & 8 ~h = R & h = R 8 array aligned & Given V = Ve 3 & h = R [ V _ e V _ e / 3 ]^2-1 = R 9-1 = R 8 aligned