A body is projected vertically upwards from earth's surface. If velocity of projection is ( 1 3 )^ rd of escape velocity, then the height upto which a body rises is ( R = radius of earth )

Step-by-step solution

V = 1 3 2 GM R TE _ At surface = TE _ at height h - G M m R + 1 2 m v²=- G M m R+h +0- G M m R + 1 2 m 1 9 2 G M R =- G M m R+h ( 1 9 -1 ) G M m R =- G M m R+h - 8 9 G M m R =- G M m R+h 8 9 1 R = 1 R+h 8 R +8 h =9 R 8 h=R h= R 8