Question

A cubical block of side $0.5m$ floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water $=10^{3}kg/m^3$ ]

• A. $87.5kg$
• B. $65.4kg$
• C. $30.1kg$
• D. $46.3kg$

Answer 1

Answer: (A)

In first case, when $30\%$ of the cube inside water,
${\rho }_w{V}_{in}g={\rho }_{c}Vg$
$\frac{V_{in}}{V}=\frac{{\rho }_c}{{\rho }_w}=0.3$
Additional weight we can put $w$ is,
$V{\rho }_{w}g={\rho }_{c}Vg+w$
$w=V\left({\rho }_W-{\rho }_c\right)g$
$={\left(0.5\right)}^3\times 0.7\times {\left(10\right)}^3\times g$
$=87.5gN$
Addition of mass that we can put $=87.5kg$