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JEE Main 2023 (1 Feb, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2023 (1 Feb, Shift 1)

Q43JEE Main 2023 · 1 FEB · SHIFT 1Medium

Rolling Motion

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^\circ$ and length $60\text{ cm}$ . If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is __________ $\text{ms}^{-1}$ . (Given $g = 10\text{ ms}^{-2}$ )

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

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Answer: 2

Height $h = L\sin 30^\circ = 0.6 \times 0.5 = 0.3$ m.
Rolling solid cylinder: $mgh = \frac{3}{4}mv^2 \Rightarrow v^2 = \frac{4}{3}gh$ .
$v^2 = \frac{4}{3}\times 10 \times 0.3 = 4$
$v = 2$ m s $^{-1}$ .

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