Question

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

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

Answer 1

Answer: (B)

Acceleration of cylinder down the plane is
$a=(g\,sin\,30^{\circ})(sin\,30^{\circ})$
$=10 \left(\frac{1}{2}\right)\left(\frac{1}{2}\right)$
$=2.5\,m/s^{2}$
time taken: $t=\sqrt{\frac{2s}{a}}$
$=\sqrt{\frac{2\times5}{2.5}}=2\,s$