Mercury is filled in a tube of radius $2 \,cm$ up to a height of $30 \,cm$. The force exerted by mercury on the bottom of the tube is . . . . . . $N$.
(Given: atmospheric pressure $P_0 = 10^5 \,N/m^2$,density of mercury $\rho = 1.36 \times 10^4 \,kg/m^3$,$g = 10 \,m/s^2$,$\pi = \frac{22}{7}$)

$A$ large vessel of height $H$ is filled with a liquid of density $\rho$ up to the brim. $A$ small hole of radius $r$ is made at the side vertical face,close to the base. The horizontal force required to stop the gushing of liquid is ...........

Water is filled to a height $H$ behind a dam of width $w$. The resultant force on the dam is ..............

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

$A$ tube of length $50\,cm$ is filled completely with an incompressible liquid of mass $250\,g$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega = x \sqrt{F} \text{ rad } s^{-1}$. If $F$ is the force exerted by the liquid at the other end,then the value of $x$ will be:

$A$ jet of liquid of cross-sectional area $a$ strikes a wall making an angle $\theta$ with the wall. The liquid strikes the wall with velocity $v$ and rebounds elastically. If the density of the liquid is $\rho$,the normal force on the wall is: