The temperature of an air bubble while rising from the bottom to the surface of a lake remains constant, but its diameter is doubled. If the pressure on the surface is $h$ meters of mercury column and the relative density of mercury is $\rho$, then the depth of the lake is: (in $\rho h$)

$A$ fluid container containing a liquid of density $\rho$ is accelerating upward with acceleration $a$ along an inclined plane of inclination $\alpha$ as shown. Then the angle of inclination $\theta$ of the free surface is:

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:
$(A)$ $d_A < d_F$
$(B)$ $d_B > d_F$
$(C)$ $d_A + d_B = 2d_F$
$(D)$ $d_A > d_F$

The cross-sectional area of a horizontal tube increases along its length linearly as we move in the direction of flow. The variation of pressure, as we move along its length in the direction of flow ($x$-direction), is best depicted by which of the following graphs?

The heart of a man pumps $5 \, \text{litres}$ of blood through the arteries per minute at a pressure of $150 \, \text{mm}$ of mercury. If the density of mercury is $13.6 \times 10^3 \, \text{kg/m}^3$ and $g = 10 \, \text{m/s}^2$, then the power (in $\text{watt}$) is:

The rate of diffusion is