A liquid is kept in a cylindrical vessel which is being rotated a… - Vidyadip

MCQ

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $ r $ and angular velocity of rotation is $\omega $, then the difference in the heights of the liquid at the centre of the vessel and the edge is

A
$\frac{{r\omega }}{{2g}}$
✓
$\frac{{{r^2}{\omega ^2}}}{{2g}}$
C
$\sqrt {2gr\omega } $
D
$\frac{{{\omega ^2}}}{{2g{r^2}}}$

✓

Answer

Correct option: B.

$\frac{{{r^2}{\omega ^2}}}{{2g}}$

b
(b)From Bernoulli's theorem,
${P_A} + \frac{1}{2}dv_A^2 + dg{h_A} = {P_B} + \frac{1}{2}dv_B^2 + dg{h_B}$
Here, ${h_A} = {h_B}$
$\therefore \;{P_A} + \frac{1}{2}dv_A^2 = {P_B} + \frac{1}{2}dv_B^2$
==> ${P_A} - {P_B} = \frac{1}{2}d[v_B^2 - v_A^2]$
Now, ${v_A} = 0,\;{v_B} = r\omega $ and ${P_A} - {P_B} = hdg$
$\therefore \;\;hdg = \frac{1}{2}d{r^2}{\omega ^2}$ or $h = \frac{{{r^2}{\omega ^2}}}{{2g}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 9.1 , fluid mechanics→9.1 , fluid mechanics — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A small speaker delivers $2\, W$ of audio output. At what distance from the speaker will one detect $120\, dB$ intensity sound ... $cm$ ? [Given reference intensity of sound as $10^{-12}\,W/m^2$]

A body is projected from earth's surface to become its satellite. Its time period of revolution will not depend upon:

The dimension of Planck constant equals to that of

The number of degrees of freedom for translatory motion are:

The density of a rod gradually decreases from one end to the other. It is pivoted at an end so that it can move about a vertical axis through the pivot. A horizontal force F is applied on the free end in a direction perpendicular to the rod. The quantities, that do not depend on which end of the rod is pivoted, are:

A sphere cannot roll on:

A particle executes $SHM.$ Its velocities are $v_1$and $v_2$ at displacement $x_1$ and $x_2$ from mean position respectively. The frequency of oscillation will be

A body is moving with velocity $30\; m/s$ towards east. After $10$ seconds its velocity becomes $40\; m/s$ towards north. The average acceleration of the body is ...... $m/s^2$

The top of a water tank is open to air and its water level is maintained. It is giving out $0.74\,m^3$ water per minute through a circular opening of $2\,cm$ radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ $m$

The horizontal range of a projectile fired at an angle of 15° is 50m. If it is fired with the same speed at an angle of 45°, its range will be

60m
71m
100m
141m