Question

An inclined plane makes an angle ${30}^0$ with horizontal. A groove OA=5cm cut on the plane makes an angle ${30}^0$ with OX, A short smooth cylinder is free ti slide down the groove under the influence of gravity. the time taken by the cylinder to reach from A to O is $(g=10m/s^2)$

• A. $4s$
• B. $10s$
• C. $2s$
• D. $5s$

Answer 1

The correct option is C $2s$

$\begin{array}{c}Theplaneisinclinedat{30}^{0}tohorizontalandthepathofthecylinderisat{30}^{0}toOX\\ thereforetheaccelerationofcylinder\\ a=\left(g\sin {30}^0\right)\left(\sin {30}^0\right)\\ =10\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\\ =2.5m/s\\ timetaken=t=\sqrt{\frac{2s}{a}}\\ =\sqrt{\frac{2\times 5}{2.5}}=2s\end{array}$

Hence,

option $\left(C\right)$ is correct answer.