91Ó°ÊÓ

Graph: Gauge pressure$\left(P_g\right)$ versus depth$\left(d\right)$ is plotted for the liquids.

The buoyant force is proportional to the density of fluid and acceleration due to gravity if the volume is constant. The slope of gauge pressure versus depth graph gives the value of the product of the density and gravitational acceleration of the body.

Formulae:

The buoyant force applied on a block by the fluid, $F_B=\mathrm{ÒÏ}Vg$ (i)

The gauge pressure acting on a body, $P_g=\mathrm{ÒÏ}gh$ (ii)

Here, the volume of a submerged bead is constant.

Thus, from equation (i), we can get that

$F_B\mathrm{Î\pm }\mathrm{ÒÏ}g....................\left(a\right)$

From equation (ii), the slope of gauge pressure versus depth gives the value of

$\mathrm{ÒÏ}g\frac{P_g}{h}\mathrm{ÒÏ}g$

As slope is greatest for $P_g$versus $h$graph, the buoyant force would be greatest considering equation (a).

Therefore, rank of buoyant force is $F_a>F_b>F_c$.