Question

A rubber ball floats on water with its $\frac{1}{3}rd$ volume outside water. What is the density of rubber ?

Answer 1

Let 'g' be the acceleration due to gravity. $\rho$ be the density of water. So, $\rho$ = $\frac{1g}{c{m}^3}$ .
'V' be the volume of the Rubber and 'q' be the density of the Rubber.

Volume of Rubber within water = V – $\frac{1}{3}V$

=$\frac{2}{3}V$

= Volume of water displaced by the Rubber

$\therefore Weightofthewaterdisplaced=\frac{2}{3}V\times \rho \times g$

Weight of the Rubber =$V\times q\times g$

Since,
Rubber is floating on the surface,

$\frac{2}{3}V\times \rho \times g=V\times \rho \times g$
$⟶q=\frac{2}{3}\rho$

That is, the density of the Rubber is $\frac{2}{3}\frac{g}{c{m}^3}$