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A tunnel is dug across the earth of mass...

A tunnel is dug across the earth of mass 'M' and radius 'R' at a distance `R//2` from the centre 'O' of the Earth as shown. A body is released from rest from one end of the smooth tunnel. The velocity acquired by the body when it reaches the centre 'C' of the tunnel is

A

`sqrt((3GM)/(2R))`

B

`sqrt((3GM)/(4R))`

C

`sqrt((3GM)/(8R))`

D

`dsqrt((3GM)/(16R))`

Text Solution

Verified by Experts

The correct Answer is:
B
Using conservation of energy
`(1)/(2)mv^(2) = -(GMm)/(R ) - ((-11GMm)/(8R))`
`(1)/(2)mv^(2) = (3GMn)/(8R)`
`:. V = sqrt((3GM)/(4R))`
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