Question

Two solids P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with ${\frac{2}{3}}^{rd}$ of its volume is immersed. The ratio of densities of P and Q is.

• A. $4/3$
• B. $3/4$
• C. $2/3$
• D. $3/2$

Answer 1

Answer: (B)

$3/4$

Let the densities of $P,Q$ and water be ${\rho }_p,{\rho }_q$ and ${\rho }_w$ respectively.

For solid P immersing half of its volume in water :

$\therefore$ $\left(V\right)g{\rho }_p=\left(\frac{V}{2}\right)g{\rho }_w$ (Archimedes principle)

$⟹$ ${\rho }_w=2{\rho }_p$ ........(1)

For solid Q immersing (2/3)rd of its volume in water :

$\therefore$ $\left(V\right)g{\rho }_q=\left(\frac{2V}{3}\right)g{\rho }_w$ (Archimedes principle)

$⟹$ ${\rho }_w=\frac{3}{2}{\rho }_q$ ........(2)

From (1) and (2) we get $2{\rho }_p=\frac{3}{2}{\rho }_q$

$⟹$ $\frac{{\rho }_p}{{\rho }_q}=\frac{3}{4}$