Consider two solid spherical asteroids with same uniform density, of mass $M$  and radius R In one asteroid, a smooth tunnel of very small cross section and depth R  is bored to the centre and in other asteroid, a spherical cavity of radius $\frac{R}{2}$  is made as shown in the figure. Now, two identical particles of mass m  are dropped into the cavities of both asteroids from the top most point  P. The magnitudes of gravitational forces experienced by particles are $F_I$  and $F_{II}$  respectively in cavities of asteroids  $I$ and $II,$  when they are  x distance away from the centres of asteroids. If the times taken by particles to reach the centres of asteroids are  $T_I$ and $T_{II}$  respectively, then :