Question

A solid cylinder of density $800kg{m}^{-3}$ floats in water. The percentage volume of solid cylinder outside the water is

• A. $10$
• B. $80$
• C. $50$
• D. $20$

Answer 1

Answer: (D)

$20$

We know that, density of water is $1000{\text{kg m}}^{-3}$

Given density of the solid is $800{\text{kg m}}^{-3}$

Let the volume of cylinder be $V$ and the volume immersed in water be $V_{im}$

Weight of the cylinder is $W={\rho }_{s}Vg$

By Archimedes Principle,

Buoyancy force on the cylinder is $B={\rho }_w{V}_{im}g$

In equilibrium, net force $=0$

Thus, ${\rho }_{s}Vg={\rho }_w{V}_{im}g\Rightarrow \frac{V_{im}}{V}=\frac{{\rho }_s}{{\rho }_w}=0.8$

Thus, $V_{im}=0.8V$

Volume outside the water is $V_f=V-V_{im}=0.2V=20$%$V$