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. `m v_0^2`
B. `2 mv_0^2`
C. `(1)/(4) mv_0^2`
D. `(1)/(2) mv_0^2`

Answer

B

Explanation

( c) Initial angular momentum `L_(initial) = mv_0 R`
Initial angular momentum `L_(initial) = mv ( R)/(2)`
Conservation of angular momentum
`m v_0 R_0 =m mv (R_0)/(2) rArr v = 2 v_0`
`KE = (1)/(2) mv^2 = 2 mv_0^2`.