Questions in Mechanical Properties of Fluids

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Pressure inside two soap bubbles are $1.01$ and $1.02$ atmospheres. Ratio between their volumes is
A capillary tube of radius r is dipped in a liquid of density $\rho$ and surface tension $S$. If the angle of contact is $\theta$, the pressure difference between the two surfaces in the beaker and the capillary
The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by
The adjoining diagram shows three soap bubbles $A$, $B$ and $C$ prepared by blowing the capillary tube fitted with stop cocks, $S_1$, $S_2$ and $S_3$. With stop cock $S$ closed and stop cocks $S_1$, $S_2$ and $S_3$ opened Question Image
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is
A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is
The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is
Excess pressure of one soap bubble is four times more than the other. Then the ratio of volume of first bubble to another one is
There are two liquid drops of different radii. The excess pressure inside over the outside is
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake

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