$A$ light semi-cylindrical gate of radius $R$ and length $l$ is pivoted at its midpoint $O$ of the diameter as shown in the figure,holding liquid of density $\rho$. The force $F$ required to prevent the rotation of the gate is equal to:

$A$ cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The diameter of the vessel is $10 \, cm$ and the angular speed of rotation is $\omega \, rad \, s^{-1}$. The difference in the height,$h$ (in $cm$),of the liquid at the centre of the vessel and at the side will be

The human heart discharges $75 \ cc$ of blood per beat against a pressure of $10 \ cm$ of $Hg$. If the heart beats $72$ times per minute,calculate the power of the heart in $W$. (Given: density of $Hg = 13.6 \ g/cc$ and $g = 9.8 \ m/s^2$)

Vapour is injected at a uniform rate into a closed vessel which was initially evacuated. The pressure in the vessel:

The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. $A$ graph showing the speed $v$ with which the liquid is crossing points at a distance $X$ from $O$ along a radius $XO$ would look like:

$A$ liquid of density $\rho$ is coming out of a hose pipe of cross-sectional area $A$ with horizontal speed $v$ and hits a mesh. $50\%$ of the liquid passes through the mesh unaffected. $25\%$ loses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mesh will be