(A) Consider a small element of the liquid of length $dx$ at a distance $x$ from the axis of rotation. The mass of this element is $dM = (M/L)dx$.The

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(A) Consider a small element of the liquid of length $dx$ at a distance $x$ from the axis of rotation. The mass of this element is $dM = (M/L)dx$.The centripetal force required for this element to rotate in a circle of radius $x$ is $dF = (dM)\omega^2 x$.Substituting $dM$,we get $dF = (M/L)dx \cdot \omega^2 x = (M\omega^2/L)x dx$.The total force $F$ exerted by the liquid at the outer end is the integral of these centripetal forces from $x = 0$ to $x = L$:$F = \int_0^L \frac{M\omega^2}{L} x dx = \frac{M\omega^2}{L} \left[ \frac{x^2}{2} \right]_0^L = \frac{M\omega^2}{L} \cdot \frac{L^2}{2} = \frac{1}{2}ML\omega^2$.

Class 11 Physics Fluid Mechanics and Surface Tension Force due to Liquid in pipe

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$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

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A
$\frac{ML\omega^2}{2}$
B
$ML\omega^2$
C
$\frac{M\omega L^2}{2}$
D
$\frac{ML^2\omega^2}{2}$

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Fluid Mechanics and Surface Tension

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Force due to Liquid in pipe

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$A$ pressure-pump has a horizontal tube of cross-sectional area $10 \, cm^{2}$ for the outflow of water at a speed of $20 \, m/s$. The force exerted on the vertical wall just in front of the tube,which stops the water horizontally flowing out of the tube,is $... N$ [Given: density of water $= 1000 \, kg/m^{3}$].

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$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is

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Water flowing through a pipe of area of cross-section $2 \times 10^{-3} \,m^2$ hits a vertical wall horizontally with a velocity of $12 \,m \,s^{-1}$. If the water does not rebound after hitting the wall, then the force acting on the wall due to water is (in $\,N$)

$A$ stream of water flowing horizontally with a speed of $15\; m s^{-1}$ gushes out of a tube of cross-sectional area $10^{-2}\; m^2$,and hits a vertical wall nearby. What is the force in $N$ exerted on the wall by the impact of water,assuming it does not rebound?

$A$ 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:

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