Q130 / 160 · AP EAMCET 2024 (23 May Shift 1) · Physics
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
- ASolid cylinder
- Correct answerBSolid sphere
- CRing
- DSolid sphere and Ring
Solution
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, $\therefore \quad \mathrm{v}_{\text {solid sphere }}\gt\mathrm{v}_{\text {solid cylinder }}\gt\mathrm{v}_{\text {ring }}$
Also, $\therefore \quad \mathrm{v}_{\text {solid sphere }}\gt\mathrm{v}_{\text {solid cylinder }}\gt\mathrm{v}_{\text {ring }}$
Hence, the correct answer is option: 'B'.