$\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,Let\,v\,be\,{\rm{tangential}}\,{\rm{speed}}\,{\rm{of}}\,{\rm{heavier}}\\
{\rm{stone}}{\rm{.}}\,{\rm{Then}}\,{\rm{,}}\,{\rm{centripetal}}\,{\rm{force}}\,{\rm{experienced}}\\
{\rm{by}}\,{\rm{lighter}}\,{\rm{stone}}\,{\rm{is}}\,\\
{\left( {{F_c}} \right)_{lighter}} = \frac{{m{{\left( {nv} \right)}^2}}}{r}\,and\,that\,of\,heavier\,stone\,is\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\left( {{F_C}} \right)_{heavier}} = \frac{{2m{v^2}}}{{\left( {r/2} \right)}}
\end{array}$
$\begin{array}{l}
But\,{\left( {{F_c}} \right)_{lighter}} = {\left( {{F_c}} \right)_{heavier}}\,(given)\\
\therefore \,\,\,\frac{{m{{\left( {nv} \right)}^2}}}{r} = \frac{{2m{v^2}}}{{\left( {r/2} \right)}}\\
\,\,\,\,\,\,\,\,\,\,{n^2}\left( {\frac{{m{v^2}}}{r}} \right) = 4\left( {\frac{{m{v^2}}}{r}} \right)\\
\,\,\,\,\,\,\,\,\,\,{n^2} = 4\,\,\,or\,\,\,n = 2
\end{array}$