The volume of an air bubble become three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be$75 \mathrm{cm}$ of$\mathrm{Hg}$and density of water to be ${\left(\frac{1}{10}\right)}^{\mathrm{th}}$ of the density of mercury, then, the depth of the lake is (assume the constant temperature of the lake)

A vertical U-tube of uniform inner cross-section contains mercury in both sides of its arms. A glycerin (density$=1.3 \mathrm{g} {\mathrm{cm}}^{-3}$) column of length$10 \mathrm{cm}$ is introduced into one of its arms. Oil of density $0.8$ $\mathrm{g} {\mathrm{cm}}^{-3}$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. (Density of mercury$=13 .6 \mathrm{g} {\mathrm{cm}}^{-3}$)

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In the figure shown, water is filled in a symmetrical container. Four pistons of equal area $A$ are used at the four openings to keep the water in equilibrium. Now an additional force $F$ is applied at each piston. The increase in the pressure at the centre of the container due to this addition is

From the figure below, the correct observation is that