Question

Two wooden blocks $A$ and $B$ float in a liquid of density ${\rho }_L$ as shown. The distance $L$ and $h$ are shown. After some time, block $B$ is kept submerged in the liquid, so that $L$ decreases and $h$ increases. If density of block $B$ is ${\rho }_B,$ then find the correct option.

• A. ${\rho }_L={\rho }_B$
• B. ${\rho }_L>{\rho }_B$
• C. ${\rho }_L<{\rho }_B$
• D. unpredictable

Answer 1

The correct option is B ${\rho }_L>{\rho }_B$

When block $B$ is kept submerged, $L$ will decrease.
Let block $B$ displaces volume of liquid $V_1$ equal to its own volume when it is in the liquid.
$V_1=V_B=\frac{M_B}{{\rho }_B}$ .......(i)

Again, when block $B$ is on block $A$, it will displace the volume of liquid $\left(V_2\right)$ whose weight is equal to the weight of the block $B$.
$\therefore V_2{\rho }_{L}g=M_{B}g=V_1{\rho }_{B}g$
$\Rightarrow V_2{\rho }_L=V_1{\rho }_B$

Since $h$ increases, $V_1>V_2$
So, ${\rho }_L>{\rho }_B$.