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System of Particles and Rotational Motion

Rolling without slipping

Two bodies, a ring and a solid cylinder of same material are r

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Solving time: 2 mins

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping and inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{x}{2}$ . Then, the value of x is _________.

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Exam:

JEE Mains 2021 July 20 Shift 2

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Two bodies, a ring and a solid cylinder of same material are rolling down without slipping and inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is

\frac{x}{2}

. Then, the value of x is _________.

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Text solutionVerified

If we consider both the bodies have same mass

\begin{aligned} &\mathrm{K} . \mathrm{E}_{\text {ring }}=\mathrm{K} . \text { E_{solid cylindor} } \\ &\frac{1}{2} \mathrm{M}_{\mathrm{R}} \mathrm{V}_{\mathrm{R}}^{2}+\frac{1}{2} \mathrm{I}_{\mathrm{R}} \omega_{\mathrm{R}}^{2}=\frac{1}{2} \mathrm{M}_{\mathrm{C}} \mathrm{V}_{\mathrm{C}}^{2}+\frac{1}{2} \mathrm{I}_{\mathrm{C}} \omega_{\mathrm{C}}^{2} \quad\left[\mathrm{I}_{\mathrm{R}}=\mathrm{M}_{\mathrm{R}} \mathrm{R}^{2}, \mathrm{IC}=1 / 2 \mathrm{Mc} \mathrm{R}^{2}\right] \end{aligned}

2 M_{R} V_{R}^{2} = \frac{3}{2} M_{C} V_{C}^{2}

[considering

M_{R} = M_{c}

]

\frac{V _{R}}{V _{C}} = \frac{3}{2}

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Question Text	Two bodies, a ring and a solid cylinder of same material are rolling down without slipping and inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{x}{2}$ . Then, the value of x is _________.
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	29

Text solutionVerified

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