Question

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

• A. 4 s
• B. 2 s
• C. 3 s
• D. 1 s

Answer 1

The correct option is B 2 s

Here,

$a=gsin{30}^{\circ }$

$u=0$

$s=5m$

$g=10m/s$

Time taken by cylinder to reach from $A$ to $o$ is

$s=ut+\frac{1}{2}a{t}^2$

Substitute all value in above equation

$5=0\times t+\frac{1}{2}\times g\times sin30\times t^{2}5=\frac{1}{2}\times 5\times \frac{1}{2}{t}^2{t}^2=\frac{5\times 2\times 2}{5}t=\sqrt{2\times 2}=2s$

Hence, correct option is B.