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

Answer 1

The correct option is C $10cm$

Volume of the cube $a^3$

$(a^3{\rho }_c+200g)g=a^3{\rho }_{w}g$

In second case

Volume of the cube$=(a-2)a^2$

$\left(a^3{\rho }_{c}g\right)=(a-2)a^2{\rho }_{w}g1=\frac{a^3{\rho }_w-200}{(a-2)a^2{\rho }_w}(a-2)a^2=a^3-200[{\rho }_w=1g/cc]2a^2=200a=10cm$