\(\therefore \frac{{{\upsilon _1}}}{{{\upsilon _2}}} = \left( {\frac{{{r_1}}}{{{r_2}}}} \right)\,\left( {\frac{{{\omega _1}}}{{{\omega _2}}}} \right)\)

હવે,જો કણ ની રેખીય ઝડપ ચરગની અને કોણીય વેગ બમણો કરવામાં આવે તો \({\text{ }}{\upsilon _{\text{2}}}{\text{  =  4}}{\upsilon _{\text{1}}}\) અને \({\omega _{\text{2}}}{\text{  =  2}}\,{\omega _{\text{1}}}\) .

\(\therefore \,\frac{{{\upsilon _1}}}{{4{\upsilon _1}}} = \left( {\frac{{{r_1}}}{{{r_2}}}} \right)\,\left( {\frac{{{\omega _1}}}{{2{\omega _1}}}} \right)\,\,\,\)

\(\therefore \frac{1}{4} = \frac{{{r_1}}}{{{r_2}}}\left( {\frac{1}{2}} \right)\)

\(\therefore \frac{{{r_1}}}{{{r_2}}} = \frac{1}{2}\,\,\,\,\,\,\therefore \frac{{{r_2}}}{{{r_1}}} = 2\,\,;\,\,\,\)

હવે,કેન્દ્ર ગામી પ્રવેગ\({a_c} = r{\omega ^2}\,\,\,\,\therefore \,\frac{{{a_{{c_2}}}}}{{{a_{{c_1}}}}} = \frac{{{r_2}}}{{{r_1}}}{\left( {\frac{{{\omega _2}}}{{{\omega _1}}}} \right)^2}\,\)

\( = (2){\left( {\frac{{2{\omega _1}}}{{{\omega _1}}}} \right)^2} = 2 \times 4 = 8\)