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JEE Main 2022 (27 Jul, Shift 2) · Rolling Motion

Rolling Motion question from JEE Main 2022 (27 Jul, Shift 2)

Q50JEE Main 2022 · 27 JUL · SHIFT 2Difficult

Rolling Motion

A solid cylinder is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $4\text{ ms}^{-1}$ , is ____________ cm. (take g = $10\text{ ms}^{-2}$ )

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

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Answer: 120

The cylinder unwinds like a yo-yo (rolling on the strings), $k = \frac{1}{2}$ .
$mgh = \frac{1}{2}mv^2\left(1+\frac{1}{2}\right) \Rightarrow h = \dfrac{3v^2}{4g}$ .
$h = \dfrac{3 \times 16}{40} = 1.2$ m $= 120$ cm.

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