A body is projected vertically upwards from the surface of a planet of radius (R ) with a velocity equal to half the escape velocity of that planet. Then, the maximum height attained by the body is

Step-by-step solution

If a body is projected vertically upwards with a velocity of (v ) from the surface of planet, then maximum height attained by the body is (h= v^2 R 2 g R-v^2 ) ...(i) But given that, ( aligned v & = v_e 2 = 2 g R 2 v^2= 2 g R 4 v^2 & = g R 2 (ii) aligned ) From Eqs. (i) and (ii), we get (h= g R 2 R 2 g R- g R 2 = g R^2 2 3 g R 2 h= R 3 )