$A$ bubble from the bottom of a lake rises to its surface. Its volume doubles in the process. Assuming isothermal conditions, atmospheric pressure $= 75 \, cm$ of $Hg$, and the ratio of the densities of mercury and water $= 40/3$. The depth of the lake will be ..... $m$.

$A$ triangular lamina of area $A$ and height $h$ is immersed in a liquid of density $\rho$ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is

In the arrangement shown, both the vessels $A$ and $B$ are identical, but the amount of water in $B$ is double that in $A$. The vessels are closed by identical leak-proof pistons at the same height. The pistons are connected to the ends of a lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now, the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube?

Why is walking barefooted on a sharp gravel (grit) road difficult?

$Assertion$ : Specific gravity of a fluid is a dimensionless quantity.
$Reason$ : It is the ratio of density of fluid to the density of water at $4^{\circ}C$.

$A$ person of height $1.65 \,m$ is standing upright. The additional external force required by a blood vessel of length $1 \,cm$, diameter $1 \,mm$ at the feet to balance the pressure compared to a similar blood vessel in the head is (Density of blood $= 1.1 \times 10^3 \,kg \,m^{-3}$, $g = 10 \,ms^{-2}$) (in $\,N$)