Question

An inclined plane makes an angle ${30}^o$ with the horizontal. A grove ($OA$) of length $5m$ cut in the plane makes. an angle ${30}^o$ with OX. A short smooth cylinder is free to slide down under the influence of gravity. The time taken by the cylinder to reach from A to O ($g=10{ms}^{-2}$):

• A. $4s$
• B. $2s$
• C. $3s$
• D. $1s$

Answer 1

The correct option is B $2s$

The plane is inclined at ${30}^{\circ }$ to the horizontal and the path of the cylinder is ${30}^{\circ }$ to OX, The acceleration will be:

$\begin{array}{c}a=\left(g\sin {30}^{{}^{\circ }}\right)\sin {30}^{{}^{\circ }}\\ =10\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)=2.5m{s}^{-2}\\ Timetaken,\\ t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 5}{2.5}}=2s\end{array}$