Question

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

• A. 6 cm
• B. 8 cm
• C. 10 cm
• D. 12 cm

Answer 1

Answer: (C)

Mass $\times g=$ Volume of part of cube $\times \rho \times g$
$\Rightarrow 200\times g=L^2\left(2\times {\rho }_w\times g\right)$
$\Rightarrow 100=L^2\left\{\because {\rho }_w=1\right\}$
$\Rightarrow 10cm=L$
From the two figures we can see that the $200gm$ block is provided with required buoyant force but a part of cube which is afloat in $2^{\text{nd }}$ figure.