The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s² . The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML² /12). At this instant, the magnitude of angular acceleration (in radian/s² ) of the rod is ____________.

A $$60$$ $$mm$$ $$-$$ diameter water jet strikes a plate containing a hole of $$40mm$$ diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is $$1000$$ $$kg/{m^3}$$ . If velocities are as indicated in the figure, the magnitude of horizontal force (in $$N$$) required to hold the plate is _______________

Consider a laminar flow at zero over a flat plate . The shear stress at the wall is denoted by $${\tau _w}.$$ The axial positions $${x_1}$$ and $${x_2}$$ on the plate are measured from the leading edge in the direction of flow. If $${x_2} > {x_1},$$ then

The arrangement shown in the figure measures the velocity $$V$$ of a gas of density $$1kg/{m^3}$$ flowing through a pipe. The acceleration due to gravity is $$9.81m/{s^2}.$$ If the manometric fluid is water (density $${1000kg/{m^3}}$$ ) and the velocity $$V$$ is $$20 m/s,$$ the differential head $$h$$ (in $$mm$$) between the two arms of the manometer is ______.