Damion Ellis

2023-02-20

An inclined plane makes an angle ${30}^{\circ}$ with the horizontal. A groove OA=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. Find the time taken by the cylinder to reach from A to O.(Take $g=10m/{s}^{2}$)

A. 1 s

B. 2 s

C. 3 s

D. 4 s

A. 1 s

B. 2 s

C. 3 s

D. 4 s

Joanna Sosa

Beginner2023-02-21Added 2 answers

The acceleration of gravity acting on the cylinder is due to the inclined plane is $g\mathrm{sin}{30}^{\circ}=\frac{g}{2}m/{s}^{2}$.

Now, as the groove is making 30∘ with OX, the acceleration with which the cylinder is sliding down the plane is given by

$a=\frac{g}{2}\mathrm{cos}{60}^{\circ}=\frac{g}{4}m/{s}^{2}$

Now, using equation of motion we get,

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

$\Rightarrow 5=0+\frac{1}{2}\times \frac{g}{4}{t}^{2}$

$\Rightarrow t=2sec$

Now, as the groove is making 30∘ with OX, the acceleration with which the cylinder is sliding down the plane is given by

$a=\frac{g}{2}\mathrm{cos}{60}^{\circ}=\frac{g}{4}m/{s}^{2}$

Now, using equation of motion we get,

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

$\Rightarrow 5=0+\frac{1}{2}\times \frac{g}{4}{t}^{2}$

$\Rightarrow t=2sec$