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A thin spherical shell of total mass M a...

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 a distance `R` from the hole along a line that passes through the hole and also through the centre of the shell. This mass subsequently moves under the gravitational force of the shell. How long does the mass take to travel from the hole to the point diametrically opposite.

Text Solution

Verified by Experts

The correct Answer is:
`2xxsqrt(R^(3)//GM)`
velocity at the moment entering the hole from conservation of energy.
`U_(i)+K_(i)=U_(f)+K_(f)`
`-(GMm)/(2R)+0=-(GMm)/R+1/2mv^(2)impliesv=sqrt((GM)/R)`
Since inside no gravitational field so `v` is constant
`t=(2R)/v=2sqrt((R^(3))/(GM))`
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