ચકગતિ ઉર્જા \({E_K} = \,\,\frac{1}{2}\,\,I{\omega ^2}\,\)

\(\therefore \,\,\frac{L}{{{E_K}}}\,\, = \,\,\frac{{I\omega }}{{\frac{1}{2}\,I{\omega ^2}}}\,\, = \,\,\frac{2}{\omega }\,\,\,\,\,\therefore \,\,L\,\, = \,\,\frac{2}{\omega }\,\,{E_K}\)

આથી \(\,\frac{{{L_1}}}{{{L_2}}}\,\, = \,\,\,\frac{{2\,{E_{K1}}}}{{{\omega _1}}}\,\, \times \,\,\,\frac{{{\omega _2}}}{{2{E_{k2}}}}\,\,\, = \,\,\,\frac{{{E_{K1}}}}{{{E_{K2}}}}\,\,\, \times \,\,\,\frac{{{\omega _2}}}{{{\omega _1}}}\,\,\,\,\)

\( = \,\,\frac{{{E_{K1}}}}{{\frac{{{E_{K1}}}}{2}}}\,\, \times \,\,\frac{{2{\omega _1}}}{{{\omega _1}}}\,\,\,\,\, = \,\,2\,\, \times \,\,2\,\,\,\, = \,\,4\)

\(\therefore \,\,\,{L_2} = \,\,\frac{{{L_1}}}{4}\)