Question

The condition for a body having density ${\rho }_b$ to float completely immersed in the liquid having density ${\rho }_L$ is

• A. ${\rho }_b>{\rho }_L$
• B. ${\rho }_b<{\rho }_L$
• C. ${\rho }_b={\rho }_L$
• D. $\text{Only when}{\rho }_b=P_L=1000{\text{kg/m}}^3$

Answer 1

The correct option is C ${\rho }_b={\rho }_L$

To make body float completely immersed, upthrust should balance the weight of body.


$F_b=mg$
$\Rightarrow V_l{\rho }_{l}g=V_b{\rho }_{b}g...\left(i\right)$
where $V_b=$ volume of body
$V_l=$ volume of liquid displaced

In case of completely immersed body, volume of liquid displaced will be equal to volume of body.
$V_b=V_l$
From eq. $\left(i\right)$ we get,
${\rho }_b={\rho }_l$

Hence, density of both body and liquid should be equal, for it to float completely submerged.