One ring, one solid sphere and one solid cylinder are rolling down on same inclined plane starting from rest. The radius of all the thee are equal, The object reaches down with maximum velocity is

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Aicharya · Accepted Answer

For rolling on inclined plane, $\begin{aligned} & \mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{K}^2}{\mathrm{R}^2}} \\ & \therefore \mathrm{a}_{\text {ring }}=\frac{\mathrm{g} \sin \theta}{1+1}=\frac{1}{2} \mathrm{~g} \sin \theta=0.5 \mathrm{~g} \sin \theta \\ & \mathrm{a}_{\text {solid sphere }}=\frac{\mathrm{g} \sin \theta}{1+\frac{2}{5}}=\frac{5}{7} \mathrm{~g} \sin \theta=0.71 \mathrm{~g} \sin \theta \\ & \mathrm{a}_{\text {solid cylinder }}=\frac{\mathrm{g} \sin \theta}{1+\frac{1}{2}}=\frac{2}{3} \mathrm{~g} \sin \theta=0.66 \mathrm{~g} \sin \theta \end{aligned}$
Also, $\therefore \quad \mathrm{v}_{\text {solid sphere }}\gt\mathrm{v}_{\text {solid cylinder }}\gt\mathrm{v}_{\text {ring }}$

One ring, one solid sphere and one solid cylinder are rolling down on same inclined plane starting from rest…

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