Choose the correct option:

A solid floats with $\frac{1}{4}th$ of its volume above the surface of the water. 

The density of the solid is _____.

The volume of the solid body outside the water =$\frac{\mathrm{V}}{4}$

$$\begin{gathered} \therefore \text{ Volume of solid body inside water } \\ =\mathrm{V}-\frac{\mathrm{V} }{4}=3 \frac{\mathrm{V}}{4} \end{gathered}$$

Weight of water displaced by solid: Mass x Acceleration due to gravity

 $\mathrm{Weight} \mathrm{of} \mathrm{the} \mathrm{body} =\mathrm{V} \times \mathrm{\rho } \times \mathrm{g}$

We know that when an object is partially or fully floating in fluid, it displaces an equal volume of fluid.

The volume of displaced water =$3\frac{\mathrm{V}}{4}$

Density of water= 1000 = 10³ kg/m³

$\therefore$$\mathrm{Weight} \mathrm{of} \mathrm{the} \mathrm{water} \mathrm{displaced}=\frac{3V}{4}\times {10}^3\times g$

According to Archimedes' principle,

Weight of body = Weight of water displaced by it

$\therefore$$V\rho g=\frac{3V}{4}\times {10}^3\times g$

$\therefore$$\rho =\frac{3}{4}\times 1000=750 \mathrm{kg}{ \mathrm{m}}^{-3}$