A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}}$ in SI unit. The value of $\alpha$ is _________.

A particle is moving in a circle of radius $$50 \mathrm{~cm}$$ in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at $$\mathrm{t}=0$$ is $$4 \mathrm{~m} / \mathrm{s}$$, the time taken to complete the first revolution will be $$\frac{1}{\alpha}\left[1-e^{-2 \pi}\right] \mathrm{s}$$, where $$\alpha=$$ _________.

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $$t(1-e^{-\pi/2})s$$. The value of t is ____________.