Question

A cylinder of relative density ${\rho }_r<1$ and height $h$ floats in water with its axis vertical. The height of cylinder submerged is .

• A. ${\rho }_{r}h$
• B. $h$
• C. $h/{\rho }_r$

Answer 1

The correct option is A ${\rho }_{r}h$

Fraction of volume of cylinder submerged is given by:
$n=\frac{{\rho }_{cylinder}}{{\rho }_{water}}$
$⟹n={\rho }_r$

Let volume submerged be ${}^{\prime }{V}^{\prime }$ and height submerged be ${}^{\prime }{h}^{\prime }$.
$n=\frac{V^{\prime }}{V}$
$n=\frac{\pi r^2{h}^{\prime }}{\pi r^{2}h}$
$⟹h^{\prime }=nh={\rho }_{r}h$