Question

An inclined plane makes an angle ${30}^0$ with the horizontal. A groove OA $=5m$ cut in the plane makes an angle ${30}^0$ 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. ( $g=10m/s^2$)

• A. $8sec$
• B. $6sec$
• C. $2sec$
• D. $3sec$

Answer 1

Answer: (C)

$2sec$

As is clear from the diagram:
Component of gravity along the incline $=gsin{30}^o$
$=10\times 0.5=5m/s^2$
Component of gravity along lone OA $=\left(gsin{30}^o\right)sin{30}^o$
$=10\times 0.5\times 0.5=2.5m/s^2$
Thus acceleration of the cylinder is $2.5m/s^2$ along line OA.
Using $s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 5=\frac{1}{2}\times 2.5\times t^2$
Solving $t=2sec$
Thus (c) is the correct option.