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

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answer is 2.

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Detailed Solution

$mgh = \frac{1}{2} {mv}^{2} + \frac{1}{2} {Iω}^{2}$ (Energy conservation)
$v = ωr$ (for pure rolling)
$v = \sqrt{\frac{4 gh}{3}} = \sqrt{\frac{4 \times 10 \times 0.3}{3}} = 2 m / s .$

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