c
\(  mg\,\, - T\,\, = \,\,ma\,\,\,\,\,\,\,\,\,\,\,\,\,\,..................\left( 1 \right)\)

\(  \tau \,\, = \,\,1\,\, \propto \,\,\,\,\therefore \,\,\,T.R.\,\, = \,\,\,I.\,\,\frac{a}{2}\,\,\)

\(\therefore \,\,T\,\, = \,\,\frac{{Ia}}{{{R^2}}} \)

  From \(\,\,\left( 1 \right) \)

\(  mg\,\, = \,\,\frac{{Ia}}{{{R^2}}}\,\, + \;\,ma\,\,\,\,\)

\(\therefore \,\,\,\,a\,\, = \,\,\frac{{mg{R^2}}}{{\left( {I\,\, + \;\,m{R^2}} \right)}}\)

\(  {v^2}\,\, = \,\,{u^2}\,\, + \;\,2as\,\,\,\,\therefore \,\,\,\,u\,\, = \,\,0 \)

\(  v\,\, = \,\,\sqrt {2ah} \,\, \Rightarrow \,\,v\,\, = \,\,\sqrt {\frac{{2mgh{R^2}}}{{1\,\, + \;\,m{R^2}}}} \)