JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Rotational Mechanics

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Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity 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 ____.

Answer: 3

Solution

For a body rolling down without slipping through a height

h

, energy conservation gives

v = \frac{2 g h}{1 + \frac{k ^{2}}{R ^{2}}}

A ring has

\frac{k ^{2}}{R ^{2}} = 1

and a solid cylinder has

\frac{k ^{2}}{R ^{2}} = \frac{1}{2}

, so

\frac{v _{ring}}{v _{cyl}} = \frac{1 + \frac{1}{2}}{1 + 1} = \frac{3}{4} = \frac{3}{2}

Comparing with

\frac{x}{2}

gives

x = 3

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Integer answer

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