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 radius of vessel is $5\, cm$ and the angular speed of rotation is $\omega\; rad \,s^{-1}$. The difference in the height, $h($ in $cm )$ of liquid at the centre of vessel and at the side will be
JEE MAIN 2020, Diffcult
Download our app for free and get started
Applying pressure equation from $A$ to $B$
$P_{0}+\rho \cdot \frac{R \omega^{2}}{2} \cdot R-\rho g h=P_{0}$
$\frac{\rho R ^{2} \omega^{2}}{2}=\rho gh$
$h =\frac{ R ^{2} \omega^{2}}{2 g }=(5)^{2} \frac{\omega^{2}}{2 g }=\frac{25}{2} \frac{\omega^{2}}{ g }$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Three liquids of densities $d,\,2d$ and $3d$ are mixed in equal proportions of weights. The relative density of the mixture isView Solution
- 2A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800$ $N$ is applied to the shaft, parallel to the sleeve, the shaft attains a speed of $1.5$ $cm/sec$. If a force of $2.4$ $kN$ is applied instead, the shaft would move with a speed of ......... $ cm/sec$View Solution
- 3A $U$ -tube of small and uniform cross section contains water of total length $4H$. The height difference between the water columns on the left and on the right is $H$ when the valve $K$ is closed. The valve is suddenly open, and water is flowing from left to right. Ignore friction. The speed of water when the heights of the left and the right water columns are the same, is :-View Solution
- 4If two liquids of same volume but different densities ${\rho _1}$ and ${\rho _2}$ are mixed, then density of mixture is given byView Solution
- 5Water flows in a streamlined manner through a capillary of radius $'a'$, the pressure difference being $'p'$ and the rate of flow $Q$. If the radius is reduced to $'a/2'$ and the pressure increased to $'4p'$, the rate of flow becomes :-View Solution
- 6A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$ as shown. Then the angle of inclination $ \theta $ of free surface is :View Solution
- 7Two spheres $P$ and $Q$ of equal radii have densities $\rho_1$ and $\rho_2$, respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities $\sigma_1$ and $\sigma_2$ and viscosities $\eta_1$ and $\eta_2$, respectively. They float in equilibrium with the sphere $P$ in $L_1$ and sphere $Q$ in $L _2$ and the string being taut (see figure). If sphere $P$ alone in $L _2$ has terminal velocity $\overrightarrow{ V }_{ P }$ and $Q$ alone in $L _1$ has terminal velocity $\overrightarrow{ V }_{ Q }$, thenView Solution
$(A)$ $\frac{\left|\overrightarrow{ V }_{ P }\right|}{\left|\overrightarrow{ V }_{ Q }\right|}=\frac{\eta_1}{\eta_2}$ $(B)$ $\frac{\left|\overrightarrow{ V }_{ P }\right|}{\left|\overrightarrow{ V }_{ Q }\right|}=\frac{\eta_2}{\eta_1}$
$(C)$ $\overrightarrow{ V }_{ P } \cdot \overrightarrow{ V }_{ Q } > 0$ $(D)$ $\overrightarrow{ V }_{ P } \cdot \overrightarrow{ V }_{ Q } < 0$
- 8There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^o$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{{{d_1}}}{{{d_2}}}$ isView Solution
- 9A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y $ from the top and the other is a circular hole of radius $ R$ at a depth $ 4y $ from the top. When the tank is completely filled with water the quantities of water flowing out per second from both the holes are the same. Then $ R$ is equal toView Solution
- 10If $W$ be the weight of a body of density $\rho $ in vacuum then its apparent weight in air of density $\sigma $ isView Solution