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

JEE MainJEE Main 2023System of Particles and Rotational Motion

Solution:

$v=\sqrt{\frac{2 g h}{1+\frac{k^2}{R^2}}}$
Where $h=60 \sin 30^{\circ}=30 cm$
$k^2=\frac{R^2}{2}$
$v=2\, ms ^{-1}$