Question

A metal cube of size $15cm\times 15cm\times 15cm$ and specific gravity 8.6 is submerged in a two - layered liquid, the bottom layer being mercury and the top layer being water. The percentage of the volume of the cube remaining above the interface will be approximately

• A. 68
• B. 63
• C. 40
• D. 25

Answer 1

The correct option is C 40

Let the percentage of cube remain above interface is p. The buoyancy force is ${\rho }_w\left(0.01p\right)\times {15}^{3}g+13.6{\rho }_w(1-0.01p)\times {15}^{3}g$
This will be equal to the weight of the cube = $8.6{\rho }_w{15}^{3}g$
$\therefore 0.01p+13.6(1-0.01p)=8.6$
$12.6\times 0.01p=13.6-8.6=5$
$p=39.7\%$