A wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed the cube is $2\,cm$ above water level. The side of cube is ........ $cm$
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Let mass of cube is $\mathrm{m}$ and side is a then
$(m+200) g=a^{3} \rho_{w} g$ $...(i)$
$\mathrm{mg}=\mathrm{a}^{2}(\mathrm{a}-2) \rho_{\mathrm{w}} \mathrm{g}$ $...(ii)$
$\Rightarrow \mathrm{a}^{2}(\mathrm{a}-2) \rho_{\mathrm{w}}+200=\mathrm{a}^{3} \rho_{\mathrm{w}}$
$\Rightarrow a^{2}=100 \Rightarrow a=10 \mathrm{cm}$
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