\( = {M_1} = \pi {\left( {\frac{{56}}{2}} \right)^2}m = \pi {\left( {28} \right)^2}m\)

\( = {M_1} = \pi {\left( {\frac{{42}}{2}} \right)^2}m = \pi {\left( {21} \right)^2}m\)

Mass of remaining Part \(=\) \(M-M_{1}\)

\(C.M\) of whole disc \(=\mathrm{O}\) i.e at origin

\(C.M\) of removed Plate \(=r_{1}=28-21=7 \mathrm{cm}\)

\(C.M\) of remaining Portion \(=\mathrm{r}_{2}\)

hence

\(\mathrm{M} \times \mathrm{O}=\mathrm{M}_{1} \mathrm{r}_{1}+\left(\mathrm{M}-\mathrm{M}_{1}\right) \mathrm{r}_{2}\)

\(\mathrm{M}_{1} \mathrm{r}_{1}=-\left(\mathrm{m}-\mathrm{m}_{1}\right) \mathrm{r}_{2}\)

\({r_2} = \left[ {\frac{{\left( {{M_1}{r_1}} \right)}}{{ - \left( {m - {m_1}} \right)}}} \right]\)

\( = \left[ {\frac{{\pi {{\left( {21} \right)}^2}m}}{{ - \pi {{\left( {28} \right)}^2} - \pi {{\left( {21} \right)}^2}m}}} \right] \times 7\)

\( = \left[ {\frac{{{{\left( {21} \right)}^2}}}{{\left( { - 343} \right)}}} \right] \times 7\)

\(r_{2}=-9 \mathrm{cm}\)