A body is thrown from the surface of the earth with velocity u m s - 1 . The maximum height in meter above the surface of the earth up to which it will reach is ( R = radius of the earth, g = acceleration due to gravity)

Step-by-step solution

− G M m R + 1 2 m u 2 = 0 + ( − G M m R + h ) G M R + h = G M R − u 2 2 G M ( R + h ) = 2 GM − R u 2 2 R R + h G M = 2 R 2 G M − R u 2 h = 2 G M R 2 G M − R u 2 − R = 2 G M R − 2 G M R + R 2 u 2 2 G M − R u 2 = R 2 u 2 2 G M − R u 2 = R u 2 2 g R − u 2