Question

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.

• A. 4, 2
• B. 3, 1
• C. 1, 3
• D. 2, 4

Answer 1

Answer: (A)

According to question
$120=\rho Vg\dots ..\text{ (i) }$
(where $\rho$ is density of solid)
$90=\left(\rho -{\rho }_w\right)Vg\Rightarrow {\rho }_{w}Vg=30\dots \dots \text{ (ii) }$
(where ${\rho }_w$ is density of water)
$60=\left(\rho -{\rho }_l\right)Vg\Rightarrow {\rho }_{l}Vg=60\dots ..\text{ (iii) })$
(where ${\rho }_l$ is density of liquid)
Form (i), (ii), (iii)
$\frac{\rho }{{\rho }_w}=\frac{120}{30}=\frac{4}{1}$
$\frac{{\rho }_l}{{\rho }_w}=\frac{60}{30}=\frac{2}{1}$