The figure shows a three-arm tube in which a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the cross-sectional area of each arm be $S$. When the tube rotates,the liquid level in arm $B$ drops to zero,and the liquid rises in arms $A$

Vedclass · Accepted Answer

$\sqrt{\frac{3g}{l}}$

Vedclass · Answer

(C) Let the cross-sectional area of each arm be $S$. When the tube rotates,the liquid level in arm $B$ drops to zero,and the liquid rises in arms $A$ and $C$. Since the total volume of liquid is conserved,the liquid rises by $l/2$ in arms $A$ and $C$,reaching a height of $3l/2$.The pressure at the base of arm $A$ (or $C$) is $P = P_0 + \rho g (3l/2)$.The pressure difference between the base of arm $A$ and the axis of rotation (arm $B$) provides the centripetal force for the liquid in the horizontal section of length $l$. The center of mass of this liquid column is at a distance $l/2$ from the axis.Equating the pressure difference to the centripetal force per unit area:$(P - P_0) S = (\rho S l) \omega^2 (l/2)$Substituting $P - P_0 = \rho g (3l/2)$:$\rho g (3l/2) S = \rho S l^2 \omega^2 / 2$Canceling $\rho, S,$ and $l$ from both sides:$3g/2 = l \omega^2 / 2$$\omega^2 = 3g/l$$\omega = \sqrt{\frac{3g}{l}}$

The figure shows a three-arm tube in which a liquid is filled up to a height $l$. It is now rotated at an angular frequency $\omega$ about an axis passing through arm $B$. Find the angular frequency $\omega$ at which the level of liquid in arm $B$ becomes zero.

Similar Questions

In a turbulent flow,the velocity of the liquid molecules in contact with the walls of the tube is

Which of the following phenomena is not due to surface tension?

At a speed of .......... $m/s$,the velocity head of water is equal to the pressure head of $40\, cm$ of $Hg$.

$A$ river of salty water is flowing with a velocity $2 \,m/s$. If the density of the water is $1.2 \,g/cc$, then the kinetic energy of each cubic metre of water is

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 $g = 9.8 \ m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module