Question

A cylinder is made up of a material of relative density $2$, with a height $5cm$ and area of cross section $5c{m}^2$. On immersing in a liquid it looses half of its weight. Find the density of the liquid.

Answer 1

Volume of cylinder , $V=A\times h=5\times 5=25c{m}^3$

Mass of cylinder $m=density\times volume=2\times 25=50gram$

It looses half of it weight, it means buoyancy force half the weight of cylinder

$W=mg=50\times g$

So buoyancy is $F=\frac{W}{2}=25g$

$F=V\times {\rho }_{liquid}\times g=25\times {\rho }_{liquidg}g$

on putting the value of $F$

$25{\rho }_{liquid}g=25g$

${\rho }_{liquid}=1gc{m}^{-3}$