Question

A toy duck of volume of $15c{m}^3$ and mass of $25g$ is thrown into a liquid. For the duck to sink in the liquid, the density of the liquid should be _______.

• A. $<0.667gc{m}^{-3}$
• B. $>1.667gc{m}^{-3}$
• C. $<1.667gc{m}^{-3}$
• D. $>0.667gc{m}^{-3}$

Answer 1

The correct option is C $<1.667gc{m}^{-3}$

Given:
Mass of the toy, $m=25g$
Volume of the toy, $V=15c{m}^3$
Density of the toy, $D=\frac{m}{V}=\frac{25}{15}=1.667gc{m}^{-3}$
An object sinks in a liquid if its density is greater than the density of the liquid, else, the object floats on the liquid.
$⟹$ For the toy duck to sink in the liquid, the liquid's density must be less than the toy's density.
$\therefore$ The liquid's density $<1.667gc{m}^{-3}$