$A$ 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:

$A$ gardener waters the plants using a pipe of diameter $1\,mm$. The water comes out at a rate of $10\,cm^3/s$. The reactionary force exerted on the hand of the gardener is:

$A$ 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 ...........

$A$ 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 . . . . . . .

$A$ horizontal right-angle pipe bend has a cross-sectional area of $10 \ cm^2$ and water flows through it at a speed of $20 \ m/s$. The force on the pipe bend due to the turning of water is ........ $N$.

$A$ jet of water having velocity $v = 10 \ m/s$ and stream cross-section $A = 2 \ cm^2$ hits a flat plate perpendicularly,with the water splashing out parallel to the plate. The plate experiences a force of ....... $N$.