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Q.
A piece of solid weighs $120gm$ in open air, $90gm$ in water and $60gm$ in a liquid. The relative density of solid and that of liquid are respectively.
NTA AbhyasNTA Abhyas 2022
Solution:
According to question
$
120=\rho V g \ldots . . \text { (i) }
$
(where $\rho$ is density of solid)
$
90=\left(\rho-\rho_{w}\right) V g \Rightarrow \rho_{w} V g=30 \ldots \ldots \text { (ii) }
$
(where $\rho_{w}$ is density of water)
$
\left.60=\left(\rho-\rho_{l}\right) V g \Rightarrow \rho_{l} V g=60 \ldots . . \text { (iii) }\right)
$
(where $\rho_{l}$ is density of liquid)
Form (i), (ii), (iii)
$
\frac{\rho}{\rho_{w}}=\frac{120}{30}=\frac{4}{1}
$
$
\frac{\rho_{l}}{\rho_{w}}=\frac{60}{30}=\frac{2}{1}
$