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  4. An inclined plane makes an angle 30° with the horizontal. A groove OA =5 m cut in the plane makes an angle 30° with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is ( g =10 m / s 2)

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Q. An inclined plane makes an angle $30^{\circ}$ with the horizontal. A groove OA $=5 m$ cut in the plane makes an angle $30^{\circ}$ with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from $A$ to $O$ is $\left( g =10 m / s ^{2}\right)$Physics Question Image

Laws of Motion

Solution:

Acceleration of smooth cylinder =
$\frac{m g \sin ^{2} 30^{\circ}}{m}=g \sin ^{2} 30^{\circ}=\frac{g}{4}=\frac{10}{4} $
$s=5=\frac{1}{2} \times \frac{10}{4} \times t^{2}$
$\Rightarrow t=\sqrt{\frac{10 \times 4}{10}}=2 sec$