Q1: A cylindrical vessel 40 cm high is revolved about its vertical axis so that the water touches the bottom when it just spills out. If the radius of the cylinder is 5 cm, the angular velocity of rotation, is

ANS:A - 2 rad/sec

Correct ans is 125.28 rad/sec.

Equate all in meters for ease.
The equation is:

H - y(min) = (w^2 x R^2)/(2g).
So, here y(min) =0.
Therefore 0.4 = (w^2 x .0005)/(2 x 9.81).
Solve it, you directly get an answer in rad/sec.
After solving. w= 125.28 rad/sec.
And Just covert the units. 125.28 is in rad/min. Divide by 60 to get 2 rad/sec, we will get the answer.