(C) Let the radius of the big drop be $R$. Since the volume remains constant:$27 \times (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$R^3 = 27r^3 \Righ

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(C) Let the radius of the big drop be $R$. Since the volume remains constant:$27 \times (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$R^3 = 27r^3 \Rightarrow R = 3r$. (Statement $D$ is correct.)Excess pressure inside a drop is given by $P = \frac{2T}{r}$.$P_{\text{small}} = \frac{2T}{r}$ and $P_{\text{big}} = \frac{2T}{R} = \frac{2T}{3r} = \frac{1}{3} P_{\text{small}}$. (Statement $A$ is incorrect.)Initial surface energy $U_i = 27 \times (4 \pi r^2 T) = 108 \pi r^2 T$.Final surface energy $U_f = 4 \pi R^2 T = 4 \pi (3r)^2 T = 36 \pi r^2 T$.Since $U_f Energy released $\Delta U = U_i - U_f = 108 \pi r^2 T - 36 \pi r^2 T = 72 \pi r^2 T$. (Statement $C$ is correct.)Therefore,statements $B, C,$ and $D$ are correct.

Class 11 Physics Fluid Mechanics and Surface Tension Mix Examples-Fluid Mechanics and Surface Tension

Medium

$27$ equal small water drops combine to form a big drop. If the surface tension of water is $T$ and the radius of a small drop is $r$,then:
$(A)$ The excess pressure inside the big drop is three times the excess pressure inside the small drop.
$(B)$ Surface energy decreases in this process.
$(C)$ In this process,$72 \pi r^2 T$ energy is released.
$(D)$ The radius of the big drop is $3r$.
The true statements are:

A
$(A, B, C)$
B
$(A, B, D)$
C
$(B, C, D)$
D
$(B, D)$

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Fluid Mechanics and Surface Tension

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Mix Examples-Fluid Mechanics and Surface Tension

$A$ cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The diameter of the vessel is $10 \, cm$ and the angular speed of rotation is $\omega \, rad \, s^{-1}$. The difference in the height,$h$ (in $cm$),of the liquid at the centre of the vessel and at the side will be

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$A$ 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 the 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

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Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if:
$(A)$ $d_A < d_F$
$(B)$ $d_B > d_F$
$(C)$ $d_A + d_B = 2d_F$
$(D)$ $d_A > d_F$

DifficultIIT 2011

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An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its sides,it was found that one-third of the volume of water spilled out. The acceleration was:

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

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An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its sides,it was found that one-third of the volume of water spilled out. The acceleration was:

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

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