An object is thrown vertically upwards from the surface of the earth with a velocity x times the escape velocity on the earth (x < 1) , then the maximum height to which its rises from the centre of the earth is (radius of earth is R )

Step-by-step solution

(No option is matching.) Escape velocity is v_e= 2 G M R Let object rises upto height h , when it is thrown with speed x v_e , then from conservation of energy, we get 1 2 m (x v_e )^2- G M m R =0- G M m R+h aligned & 1 2 m (x v_e )^2 = G M m R - G M m R+h & (x v_e )^2 =2 G M ( h R(R+h) ) & x^2 2 G M R = 2 G M R ( h R+h ) & x^2 = h R+h or h= R x^2 1-x^2 aligned