Question

A rectangular block of wood floats in water with two-third of it's volume immersed .when placed placed in another liquid ,it floats with half of it's volume immersed .calculate the relative density of a liduid.

Answer 1

case 1 : a rectangular block of wood floats in water with two -third of its volume immersed.

means, weight of 100% volume of object = weight of 2/3 times of volume of water

or, $mg = \frac{2}{3}V\rho_{w}g$ .....(1)

case 2 : when rectangular block is placed in another liquid it float with its half of volume immersed.

means, weight of 100% volume of object = weight of 1/2 times of volume of liquid

or, $mg = \frac{1}{2}V\rho_l g$ ......(2)

from equations (1) and (2),

$\frac{2}{3}V\rho_w g=\frac{1}{2}V\rho_l g$

or, $\frac{2}{3}\rho_w=\frac{1}{2}\rho_l$

or,$\frac{4}{3}=\frac{\rho_l}{\rho_w}$

hence, relative density of liquid is 4/3 .