Question

A cube of 3 side L floats in a liquid of density 3 times the density of cube. What length of the cube will out side the liquid?

• A. $\frac{L}{3}$
• B. $\frac{2L}{3}$
• C. $\frac{2L}{5}$
• D. $\frac{L}{5}$

Answer 1

The correct option is B $\frac{2L}{3}$

Acc. to Arctimedes Principal

$Pi=$ density of cube $=d$

${\rho }_l=density$ of liquid $=3d$

$v_i=T_0$ to $($ volume of $cube=e^3)$

$V_l=$ immersed vol. $=x{\ell }^2$

$x=$ height immersed

$\frac{V_l}{V_i}=\frac{{\rho }_i}{P_l}=\frac{1}{3}=\frac{{\ell }^{2}x}{l^3}$

$x=\frac{l}{3}$

length ourside $=l-x=l-\frac{l}{3}=\frac{2l}{3}$