A thin spherical shell of total mass M and radius R is held fixed. There is a small hole in the shell. A mass m is released from rest at a distance R from the hole along a straight line that passes through the hole and also through the centre of the shell. This mass subsequently moves under gravitational force of the shell. How long does the mass take to travel from the hole to the point diametrically opposite?
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1 Answers
1Let " 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
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