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

Options

A. `(1)/(4) mv_(0^(2)`
B. `2 mv_(0)^(2)`
C. `(1)/(2) mv_(0^(2)`
D. `m_(0)^(2)`

Explanation

Angular momentum conservation
`mv_(0) R_(0) = mv (R_(0))/(2) implies v = 2 v_(0)`
`K_(f) = (1)/(2) mv^(2) = (1)/(2) m (2 v_(0))^(2)`
`= 2 mv_(0)^(2)`