A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be (Take radius of earth = 6400 km and g = 10 ms - 2 )

Step-by-step solution

Total mechanical energy of the body at the surface of earth M i = - G M m R + 1 2 m 1 3 2 G M R 2 = - G M m R + G M m 9 R = - 8 G M m 9 R Total mechanical energy of the body at the highest point M f = - G M m R + h Using conservation of mechanical energy, M i = M f ⇒ - G M m R + h = - 8 G M m 9 R ⇒ R + h = 9 R 8 ⇒ h = R 8 = 6400 8 = 800   km