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Fluid Mechanics and Surface Tension question bank (Physics)

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Q1.

$A$ liquid kept in a cylindrical vessel is rotated about a vertical axis passing through the center of the circular base. The difference in the heights of the liquid at the center of the vessel and its edge is ($R=$ radius of vessel,$\omega=$ angular velocity of rotation,$g=$ acceleration due to gravity).

(A)

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

(B)

$\frac{R \omega}{g}$

(C)

$\frac{R \omega}{2 g}$

(D)

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

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Q2.

$A$ liquid drop of density $\rho$ is floating half-immersed in a liquid of density $d$. If $T$ is the surface tension,then the diameter of the liquid drop is ($g$ = acceleration due to gravity).

(A)

$\left[\frac{6T}{g(2\rho-d)}\right]^{1/2}$

(B)

$\left[\frac{8T}{3g(2\rho-d)}\right]^{1/2}$

(C)

$\left[\frac{12T}{g(2\rho-d)}\right]^{1/2}$

(D)

$\left[\frac{3T}{g(2\rho-d)}\right]^{1/2}$

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