Question

A man can throw a ball with a maximum speed of nearly 38 ms^-1. The man is on a planet having a uniform density of 2.9 g/cc. On throwing the ball with maximum speed, the man finds that ball just fails to return to the planet. The radius of planet is nearly; (G = 6.67 x 10^-11 SI Unit)

(1) 2.987 km

(2) 2.987 km

(3) 29.87 km

(4) 29.87 km

Answer 1

(2) 2.987 km

Since the ball thrown with a speed of 38ms^-1 just fails to return to the surface of the planet, the escape velocity (v_esp) from planet is 38 ms^-1. Let M be mass and R radius of planet. Then