The ratio of the accelerations for a solid sphere (mass 'm' and...

For solid sphere rolling without slipping on inclined plane, acceleration a_{1}=$\frac{g \sin \theta}{1+\frac{K^{2}}{R^{2}}}$ For solid sphere slipping on inclined plane without rolling, acceleration a_{2}=g \sin $\theta$ Therefore required ratio $=\frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}=\frac{1}{1+\frac{K^{2}}{R^{2}}}=\frac{1}{1+\frac{2}{5}}=\frac{5}{7}$