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  4. In the figure shown, an inclined plane makes an angle 30° with the horizontal. A groove O A=5 m cut in the plane makes an angle 30° with O X . A short smooth cylinder is free to slide down in the groove due to the influence of gravity. The time (in s) taken by the cylinder to reach from A to O, if released from rest from A, is (g=10 m / s 2)

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

Laws of Motion

Solution:

$a=g \sin ^{2} \theta$
$a=10 \times \sin ^{2} 30^{\circ}$
$=10 \times \frac{1}{4}=\frac{5}{2} m / s ^{2}$
$S=\frac{1}{2} a t^{2}$
$t=\sqrt{\frac{2 S}{a}}$
$ \Rightarrow t=\sqrt{\frac{2 \times 5}{5 / 2}}$
$=\sqrt{4}=2\, s$