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JEE Main 2021 (20 Jul, Shift 2) · Rolling Motion

Rolling Motion question from JEE Main 2021 (20 Jul, Shift 2)

Q56JEE Main 2021 · 20 JUL · SHIFT 2Medium

Rolling Motion

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 of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$ . Then, the value of x is _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Rolling from height $h$ : $v^2 = \dfrac{2gh}{1 + k^2/R^2}$ .
Ring: $v_r^2 = gh$ ; solid cylinder: $v_c^2 = \frac{4}{3}gh$ .
$\dfrac{v_r}{v_c} = \sqrt{\dfrac{3}{4}} = \dfrac{\sqrt{3}}{2}$ , so $x = 3$ .

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