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

Options

A. `sqrt((3GM)/(2R))`
B. `sqrt((3GM)/(4R))`
C. `sqrt((3GM)/(8R))`
D. `dsqrt((3GM)/(16R))`

Answer

B

Explanation

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