"An inclined plane makes an angle 30 ∘..." solved and explained

Damion Ellis

Answered question

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 = 10 m / s^{2}

)
A. 1 s
B. 2 s
C. 3 s
D. 4 s

Joanna Sosa

Beginner2023-02-21Added 2 answers

The acceleration of gravity acting on the cylinder is due to the inclined plane is

g \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} \cos 60^{\circ} = \frac{g}{4} m / s^{2}

Now, using equation of motion we get,

s = u t + \frac{1}{2} a t^{2}

\Rightarrow 5 = 0 + \frac{1}{2} \times \frac{g}{4} t^{2}

\Rightarrow t = 2 s e c

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