Question

A wooden plank immerses up to $50\%$ in water. Then what percentage of its volume immersed in a liquid of density $0.5g/{cm}^3.$

• A. $50\%$
• B. $25\%$
• C. $75\%$
• D. $100\%$

Answer 1

The correct option is D $100\%$

Given,

Density of water, ${\rho }_w=1000kg{m}^{-3}$

Density of plank,${\rho }_p$

Density of liquid, ${\rho }_L=0.5gc{m}^{-3}=500kg{m}^{-3}$

We know that,

Net force downward force = Weight – buoyancy force

Net force downward force = total weight – weight of water displaced

For equilibrium condition net downward force is zero

$0={\rho }_{p}Vg-{\rho }_w\left(0.5V\right)g$

${\rho }_p=0.5{\rho }_w=500kg{m}^{-3}$

Net force downward force = Weight – buoyancy force

Net force downward force = total weight – weight of liquid displaced

For equilibrium condition net downward force is zero

$0={\rho }_{p}Vg-{\rho }_L{V}_{1}g$

$0=500\times Vg-500\times V_{1}g$

$V_1=V$

Hence, 100 % volume immersed in liquid.