Damion Ellis

2023-02-20

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. Find the time taken by the cylinder to reach from A to O.(Take $g=10m/{s}^{2}$)
A. 1 s
B. 2 s
C. 3 s
D. 4 s

Joanna Sosa

The acceleration of gravity acting on the cylinder is due to the inclined plane is $g\mathrm{sin}{30}^{\circ }=\frac{g}{2}m/{s}^{2}$.
Now, as the groove is making 30∘ with OX, the acceleration with which the cylinder is sliding down the plane is given by
$a=\frac{g}{2}\mathrm{cos}{60}^{\circ }=\frac{g}{4}m/{s}^{2}$

Now, using equation of motion we get,
$s=ut+\frac{1}{2}a{t}^{2}$
$⇒5=0+\frac{1}{2}×\frac{g}{4}{t}^{2}$
$⇒t=2sec$

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