$A$ mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_0$ at a radius $R_0$. The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally $m$ moves in a circle of radius $\frac{R_0}{2}$. The final value of the kinetic energy is

• A
  $mv_0^2$
• B
  $\frac{1}{4}mv_0^2$
• C
  $2mv_0^2$
• D
  $\frac{1}{2}mv_0^2$