gravitation:}

Let " u " be the velocity of the ball at the point when it enters the shell .

Now , conservation of mechanical energy between the points when the motion started and where

the ball first entered the shell , gives -

- G M m 2 R = m u ²2 - G M mR

or , u = { G MR } ^{1 / 2}

As we all know , the gravitational field inside a shell is zero .

So , once the particle enters the shell , then there won ' t be any changne in its motion .

Hence , it will move with constant velocity .

So , Total Time Taken = Distance CoveredVelocity = 2 Ru = { 4 R ³G M } ^{1 / 2}

If this really is one of your assignment problems , as indicated by Nishant Sir , then I strongly advise you against it .