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(B) Let the mass of the cube be $m$ and the side length be $a$. The density of water is $\rho_w = 1\,g/cm^3$.When the $200\,g$ mass is placed on the c

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$10$

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(B) Let the mass of the cube be $m$ and the side length be $a$. The density of water is $\rho_w = 1\,g/cm^3$.When the $200\,g$ mass is placed on the cube,it floats such that the entire volume is submerged (or at the surface level). The total weight equals the buoyant force:$(m + 200)g = a^3 \rho_w g$  --- $(i)$When the mass is removed,the cube floats with $2\,cm$ above the water level. The submerged volume is $a^2(a - 2)$:$mg = a^2(a - 2) \rho_w g$  --- $(ii)$Subtracting equation $(ii)$ from equation $(i)$:$(m + 200)g - mg = a^3 \rho_w g - a^2(a - 2) \rho_w g$$200 = a^3 \rho_w - (a^3 - 2a^2) \rho_w$$200 = a^3 \rho_w - a^3 \rho_w + 2a^2 \rho_w$$200 = 2a^2 \rho_w$Since $\rho_w = 1\,g/cm^3$:$200 = 2a^2$$a^2 = 100$$a = 10\,cm$.

$A$ wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed,the cube rises $2\,cm$ above the water level. The side of the cube is ........ $cm$.

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