Question

An inclined plane makes an angle ${30}^{\circ }$ with the horizontal. A groove $OA=5\text{m}$ 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 $O$.
$(\text{Take}g=10{\text{m/s}}^2)$

• A. $1\text{s}$
• B. $2\text{s}$
• C. $3\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is B $2\text{s}$

Due to inclined plane the acceleration due to gravity acting on the cylinder is $g\sin {30}^{\circ }=\frac{g}{2}m/s^2$.
Now, as the groove is making ${30}^{\circ }$ 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,
$s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 5=0+\frac{1}{2}\times \frac{g}{4}{t}^2$
$\Rightarrow t=2\text{sec}$