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There is a smooth tunnel upto centre C o...

There is a smooth tunnel upto centre C of a solid sphere of mass 'M' and radius R.A particle of mass `m(ltltM)` is released from point P along the line CP. Find velocity of 'm' while striking at `C`.
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Text Solution

Verified by Experts

The correct Answer is:
B, C
Using mechanical energy conservation equation.
`E_(C) = E_(P) rArr K_(C) + U_(C) = K_(P) + U_(P)`
`rArr (1)/(2) m upsilon_(C)^(2) + m V_(C) = 0 - (GMm)/((R + R ))` ..(i)
Here, `V_(C) =` potential at `C` due to mass `M = - (3)/(2) (GM)/(R )`
Substituting this value in Eq. (i) and then solving we get,
`upsilon_(C) = sqrt((2GM)/(R ))`
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