Question

A solid floats with 84% of its volume in water. The density of solid is:

• A. 0.84 g cm^-3
• B. 1.6 g cm^-3
• C. 4.8 g cm^-3
• D. 8.4 g cm^-3

Answer 1

The correct option is A

0.84 g cm^-3

Explanation for the correct option

Step 1. Given data

Volume of the solid $=v$

Volume of solid immersed in water $v_i=0.84v$

Step 2. Calculation of density of the solid (${\rho }_s$)

The various forces acting on the solid in various directions are shown below

From the figure above, it is clear that

$Weightofthesolid=buoyantforce$

$mg={\rho }_{w}g{v}_i$ …………(a)

Where $m=massofthesolid={\rho }_{s}v$ …………..(b)

${\rho }_w=densityofwater$

Using equation (b) in equation (a) and using the given values, we get

$$\begin{gathered} {\rho }_s\times v\times g=0.84v\times {\rho }_w\times g \\ {\rho }_s=0.84\times {\rho }_w \end{gathered}$$

But, ${\rho }_w=1gm/c{m}^3$

$$\begin{gathered} {\rho }_s=0.84\times 1 \\ {\rho }_s=0.84gc{m}^{-3} \end{gathered}$$

The density of solid is 0.84 g/cm³.

Hence, option (c) will be correct.