A solid cylinder length is suspended symmetrically through two ma… - Vidyadip

Question

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

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Answer

From energy conservation

$mgh =\frac{1}{2} m v^{2}+\frac{1}{2} I ^{2}$

$mgh =\frac{1}{2} mv ^{2}+\frac{1}{2} \frac{ mR ^{2}}{2} \omega^{2}$

$10\,h =\frac{16}{2}+\frac{16}{4} \Rightarrow h =1.2\,m =120\,cm$

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