Water is filled in a cylindrical vessel of height $$\mathrm{H}$$. A hole is made at height $$\mathrm{z}$$ from the bottom, as shown in the figure. The value of z for which the range (R) of the emerging water through the hole will be maximum for

A metal plate of area $$10^{-2} \mathrm{~m}^2$$ rests on a layer of castor oil, $$2 \times 10^{-3} \mathrm{~m}$$ thick, whose coefficient of viscosity is $$1.55 \mathrm{~Ns} \mathrm{~m}^{-2}$$. The approximate horizontal force required to move the plate with a uniform speed of $$3 \times 10^{-2} \mathrm{~ms}^{-1}$$ is

As shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If the U-tube moves with an acceleration 'f' towards right, the difference between liquid heights between two arms of the U-tube will be, (acceleration due to gravity = g)

As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice having an area 'a'. The piston moves with a constant velocity under the action of force F. If the density of the liquid is $$\rho$$, then the speed of the liquid emerging from the orifice is, (assume $$\mathrm{A} > >$$ a)