Question

A wooden cube just floats inside water with a $200\text{g}$ mass placed on it. When the mass is removed, the cube floats with its top surface $2\text{cm}$ above water level. What is the side of the cube?

• A. $6\text{cm}$
• B. $8\text{cm}$
• C. $10\text{cm}$
• D. $12\text{cm}$

Answer 1

The correct option is C $10\text{cm}$

Initially the wooden cube was floating completely submerged with mass $200\text{g}$ placed on it.

And removal of mass caused cube to float with top surface $2\text{cm}$ above water level. This mean the weight of mass $200\text{g}$ was balanced to buoyant force provided by $2\text{cm}$ height of cube.


Let $l$ be the cube length.

Hence, $F_B=200\times {10}^{-3}g$

$\Rightarrow \rho Vg=200\times {10}^{-3}g$

$\Rightarrow 1000\times l^2\times 2\times {10}^{-2}=200\times {10}^{-3}$

$\Rightarrow l^2=100\times {10}^{-4}$

$\Rightarrow l=10\times {10}^{-2}\text{m}=10\text{cm}.$

So, option $\left(c\right)$ is correct.