Question

A rubber ball floats on water with its 1/3 volume outside water. What is the density of rubber?​

Answer 1

$\large\underline{\underline{\sf Given:}}$

• Volume of rubber is ⅓ outside of water .

$\large\underline{\underline{\sf To\:Find:}}$

• Density of rubber $\sf{(\rho_{water}}$ = ?

$\large\underline{\underline{\sf Solution:}}$

$\textsf{According\:to\: Principle\:of\: floatation\:the\:boyancy\:force\:is\:equal\:to\:weight\:of\:body}$

•°•$\large{\boxed{\sf W_{rubber}=W_{water} }}$

$\large\implies{\sf m_rg=m_wg}$

We know :- Mass = Density × Volume

•°• $\large\implies{\sf \rho_r×V_r=\rho_w×V_w }$

$\implies{\sf \rho_r×\frac{4}{3}×π×r^3=1000×\left(\frac{2}{3}×\frac{4}{3}×πr^3\right)\rho_w}$

We know :- $\sf{\rho_w=1000kg/m^3}$

$\implies{\sf \rho_r×\frac{4}{3}×π×r^3=1000×\left(\frac{2}{3}×\frac{4}{3}×πr^3\right)×1000}$

$\large\implies{\sf \rho_r=2×\dfrac{1000}{3}}$

$\large\implies{\sf \rho_w=666.6kg/m^3 }$

$\Large\underline{\underline{\sf Answer:}}$

$\large\underline{\underline{\sf Density\:of\:Rubber\:is\:666.6kg/m^3}}$