What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth = R)                               [AIIMS 2017]

SHORT CUT :    WHEN   V=VEN  then the height reached by the body h=RN2-1 From conservation of energy,12mv12-GMemR=12mv22-GMemR+HHere,v2 = 0                                   (At maximum height)∴  12mv12-GMemR=-GMemR+HSolving, we getH=R2gRv12-1=Rve2v12-1  ∵ve=2gRwhere, ve is escape velocity.Here,  v1=13ve⇒vev1=3∴  H=R9-1=R8