Question

A metallic sphere weighs $210g$ in air, $180g$ in water and $120g$ in an unknown liquid. Find the density of metal and of liquid,

Answer 1

Density$=\frac{\text{weight in air}}{\text{change in weight in water}}$

$=\frac{210}{210-180}$

$=7$

$\therefore$ Density of metal =$7g/c{m}^2$

Change in weight in a liquid

= upthrust in liquid

$=\left(V_{solid}\right)\left({\rho }_{liquid}\right)g$

or $\Delta w\alpha {\rho }_{liquid}$

$\therefore \frac{\Delta w_l}{ϵw_w}=\frac{{\rho }_l}{{\rho }_w}$

or${\rho }_l=\frac{\Delta w_l}{\Delta w_w}{\rho }_w$

$=\left(\frac{210-120}{210-180}\right)\left(1\right)gm/c{m}^3$

$=3g/c{m}^3$