A stone with mass of $$0.1$$kg is catapulted as shown in the figure. The total force $${F_x}$$ (in N) exerted by the rubber band as a function of distance $$x$$ (in m) is given by $${F_x} = 300{x^2}.$$ If the stone is displayed by $$0.1$$ m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber bad is

A streamline and an equipotential line in a flow field

Figure shows the schematic for the measurement of velocity of air (density $$ = 1.2\,\,kg/{m^3}$$ ) through a constant -area duct using a Pilot tube and a water-tube manometer. The differential head of water (density $$ = 1000\,kg/{m^3}$$) in the two columns of the manometer is $$10$$ $$mm.$$ Take acceleration due to gravity as $$9.8$$ $$m/{s^2}.$$ The velocity of air in $$m/s$$

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids $$P$$ and $$Q$$ on a flat plate are $${1 \over 2}$$ and $$2$$ respectively. The Reynolds number based on the plate length for both the flows is $${10^4}.$$ The Prandtl and Nusselt numbers for $$P$$ are $${1 \over 8}$$ and $$35$$ respectively. The Prandtl and Nusselt number for $$Q$$ are respectively