Physics - Fluid Question with Solution | TestHub

Let $L$ be the side length of the cube and ${\rho }_w$ be the density of water.

When the mass $m=200$ g is attached, the cube is fully submerged.

Buoyant force = Weight of cube + Weight of mass

${\rho }_w{L}^{3}g={\rho }_{wood}{L}^{3}g+mg$

When the mass is removed, the cube rises by 2 cm, so the submerged height is $L-2$ cm.

${\rho }_w{L}^2(L-2)g={\rho }_{wood}{L}^{3}g$

Subtracting the two equations:

${\rho }_w{L}^{3}g-{\rho }_w{L}^2(L-2)g=mg$

${\rho }_w{L}^{2}g(L-(L-2))=mg$

${\rho }_w{L}^{2}g(2)=mg$

$1g/c{m}^3\times L^2\times 2cm=200g$

$2L^2=200$

$L^2=100$

$L=10$ cm