Question

A plastic disc of diameter $22cm$ and thickness $\frac{3}{4}cm$ has a mass of $125g$. For the disc to float on a liquid, which of the following cannot be the value of density of the liquid?

• A. $1.6g{cm}^{-3}$
• B. $2.3g{cm}^{-3}$
• C. $0.4g{cm}^{-3}$
• D. $3.0g{cm}^{-3}$

Answer 1

The correct option is C $0.4g{cm}^{-3}$

Given:
Mass of the disc, $m=125g$
Diameter of the disc, $d=22cm$
Thickness of the disc, $t=\frac{3}{4}cm$

Radius of the disc:
$r=\frac{d}{2}$
$r=\frac{22cm}{2}=11cm$

Volume of the disc:
$V=\pi r^{2}t$
$V=3.14\times {11}^2\times \frac{3}{4}$
$V\approx 285.1{cm}^3$

Density of the disc:
$d=\frac{m}{V}$
$d=\frac{125}{285.1}$
$d=0.4384g{cm}^{-3}$

For the disc to float, the liquid's density (${\rho }_l$) should be greater than that of the disc, i.e. ${\rho }_l>0.4384g{cm}^{-3}$
Among the given options, only the liquid with density $0.4$ does not satisfy this and hence, the body will sink in this liquid.