Question

A woman of mass $50kg$ stands on a wooden block placed over a tank of water. The wooden block is such that the woman is entirely above water. If relative density of wood is $0.85,$ the volume of the wooden block is:

• A. $0.5\times {10}^{-2}{m}^3$
• B. $0.585\times {10}^{-1}{m}^3$
• C. $0.33m^3$
• D. $0.54\times {10}^{-3}{m}^3$

Answer 1

The correct option is C $0.33m^3$

weight needs to be balanced by force of buoyancy.
$\Rightarrow Mg+\left(\rho v\right)g=\left({\rho }_{w}v\right)g$
$\Rightarrow M=({\rho }_w-\rho )v$
$\therefore v=\frac{M}{{\rho }_w-\rho }=\frac{50}{1000-850}$
$\frac{50}{150}=0.33m^3$
relative density of wood $=0.85\Rightarrow \rho =850kg/m^3$