91Ó°ÊÓ

(a) Graph of versus $W_{app}$is plotted for all the three liquids.

(b) The rectangular block is faced down.

Using the concept of the apparent weight of a block and the buoyant force, we can get the value of the required ratio which is the weight per unit volume. The value of weight per unit volume of fluid increases with a decrease in the value of the apparent weight.

Formula:

The buoyant force applied on a body by the fluid due to its weight,$F_b=\mathrm{ÒÏ}gV$ (i)

The apparent weight of a body due to displaced volume, $W_{app}=mg-F_B$ (ii)

From equation (i), the force or the weight per unit volume of a body can be given as:

Weight per unit volume$\left(\mathrm{γ}\right)=\mathrm{ÒÏ}g.................\left(a\right)$

Substituting the value of buoyant force from equation (i) in equation (ii), we can get the apparent weight of the block as follows:

$$\begin{gathered} W_{app}=mg-\mathrm{ÒÏ}gV \\ =mg-\mathrm{γ}v \\ \mathrm{γ}=\frac{mg-W_{app}}{V}........................\left(b\right) \end{gathered}$$

From equation (b), we can say that as $W_{app}$ decreases when weight per unit volume increases.

Therefore, the rank of weight per unit volume is${\mathrm{γ}}_c>{\mathrm{γ}}_b>{\mathrm{γ}}_a$.