Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is v and the effective acceleration due to gravity on the equator is 1 3 of its value at the poles. What is the escape velocity for a particle at the pole of this planet.

Step-by-step solution

We know that the escape velocity of a particle from the surface of a planet is given by aligned v_e & = 2 G M R = 2 g R^2 R [ G M=g R^2 ] & = 2 g R aligned where, g= acceleration due to gravity, and R= radius of the planet Given, the velocity at equator, v_E=V and acceleration due to gravity at equator, aligned g_E & = 1 3 g_P g_P & =3 g_E aligned The escape velocity of a particle at equator, v_E= 2 g_E R and at poles, aligned v_P & = 2 g_P R & = 2 3 g_E R = 3 2 g_E R & = 3 v_E & = 3 v aligned [From Eq. (i)] [From