\(mvr = mv'r'\)

\({v_0}{R_0} = v\left( {\frac{{{R_0}}}{2}} \right);\,v = 2{v_0}\)
\({{{K_0}}}{K} = \frac{{\frac{1}{2}mv_0^2}}{{\frac{1}{2}m{v^2}}}\)                         

or\({K}{{{K_0}}} = {\left( {\frac{v}{{{v_0}}}} \right)^2} = {\left( 2 \right)^2}\) Using \((i)\)

\(K = 4{K_0} = 2mv_0^2\)