The total energy of a solid sphere of mass 300 g which rolls without slipping with a constant veloci

Question

The total energy of a solid sphere of mass 300 g which rolls without slipping with a constant velocity of $5 \mathrm{~ms}^{-1}$ along a straight line is\

Professor PC Thomas Classes · Answer

\ Here, mass of the sphere, $\mathrm{M}=300 \mathrm{~g}=0.3 \mathrm{~kg}$\ In case of rolling motion without slipping. Total energy, $\mathrm{K}=\mathrm{K}_{\mathrm{T}}+\mathrm{K}_{\mathrm{R}}$\ $K=\frac{1}{2} M v^{2}+\frac{1}{2} I \omega^{2}$\ $=\frac{1}{2} \mathrm{Mv}^{2}+\frac{1}{2} \frac{2}{5} \mathrm{MR}^{2} \omega^{2}$\ $\left(\becauseight.$ For solid sphere, $\left.\mathrm{I}=\frac{2}{5} \mathrm{MR}^{2}ight)$\ $=\frac{1}{2} \mathrm{Mv}^{2}+\frac{1}{5} \mathrm{Mv}^{2} \quad(\because \mathrm{v}=\mathrm{R} \omega)$\ $=\frac{7}{10} \mathrm{Mv}^{2}=\frac{7}{10} 	imes 0.3 	imes 5^{2}=5.25 \mathrm{~J}$\