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A mass m moves in a circles on a smooth ...

A mass `m` moves in a circles on a smooth horizontal plane with velocity `v_(0)` at a radius `R_(0)`. The mass is atteched to string which passes through a smooth hole in the plane as shown.
The tension in string is increased gradually and finally `m` moves in a cricle of radius `(R_(0))/(2)`. the final value of the kinetic energy is

A

`(1)/(4)mv_(0)"^(2)`

B

`2mv_(0)^(2)`

C

`(1)/(2)2mv_(0)^(2)`

D

`mv_(0)^(2)`

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