Question

A cube of wood supporting $200gm$ mass just in water $(\rho =1g/cc)$. When the mass is removed, the cube rises by $2cm$. The volume of cube is

• A. $1000cc$
• B. $800cc$
• C. $500cc$
• D. None of these

Answer 1

The correct option is D None of these

Let the edge of cube be $L$ when mass is on the cube of wood

$200g+L^3{d}_{wood}g=L^3{d}_{water}g$

$\Rightarrow L^3{d}_{wood}g=L^3{d}_{water}g$

$\Rightarrow L^3{d}_{wood}g=L^3{d}_{water}g-200g$

$\Rightarrow L^3{d}_{wood}=L^{3}d-200$

When mass is removed

$L^3{d}_{wood}-(L-2)L^2{d}_{water}⟶\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$L^3{d}_{water}-200=(L-2)L^2{d}_{water}$

But $d_{water}=1$

$\therefore$ $L^3-200=L^2(L-2)$

$\therefore$ $L=10cm$.