Question

a wooden block of mass 400 gram float vertically in a liquid of density 0.8 gram/cm cube... if the volume of the block is 625 cm cube....find the volume of the block above the surface of the liquid

Answer 1

Given:

A wooden block of mass 400 gram float vertically in a liquid of density 0.8 gram/cm cube. The volume of the block is 625 cm³.

To find:

Volume of block above liquid surface ?

Calculation:

In case of floating, the weight of the block is being balanced by the buoyant force:

$\therefore \: F_{b} = mg$

$\implies \: (V_{inside}) \rho g = (V_{total}) \sigma g$

$\implies \: \dfrac{V_{inside}}{V_{total}} = \dfrac{ \sigma}{ \rho}$

$\implies \: \dfrac{V_{inside}}{625} = \dfrac{ (\frac{400}{625} )}{ 0.8}$

$\implies \: \dfrac{V_{inside}}{625} = \dfrac{ 0.64}{ 0.8}$

$\implies \: \dfrac{V_{inside}}{625} = 0.8$

$\implies \: V_{inside} = 500 \: {cm}^{3}$

$\implies \: V_{outside} =(625 - 500 )\: {cm}^{3}$

$\implies \: V_{outside} =125 \: {cm}^{3}$

So, volume outside liquid is 125 cm³.