find the time taken

We have to first resolve the gravitational force mg into 2 components one in that slant plane & another normal to that plane.

The component in that plane will be mg Sin30°

The other normal component will be mg Cos30° but we are least interested in that.

Now again we have to resolve mg Sin30° into 2 component, the component in the direction OA will be mg Sin30° * Cos60°

Only this componet of force will cause motion in the cylinder.

So, Accelearation = g Sin30° * Cos60° = g * 1/2 * 1/2 = 2.5 m/s²

Just 1 line of calculation after this..... [1]
Cheers

I am not able to visualize how you have taken the two components.
Please explain a bit more

Try to think logically, you will get it.

I didn't put the picture of resolved forces coz that would be spoon feeding [1]

Think .... think ...