Question

The volume of a $500g$ sealed packet is $350c{m}^3$. Will the packet float or sink in water if the density of water is $1gc{m}^{-3}$? What will be the mass of the water displaced by this packet?

Answer 1

Step 1: Given data

Mass, $m=500g$

Volume, $V=350c{m}^3$

Density of water, ${\rho }_w=1gc{m}^{-3}$

Step 2: Concept

1. If the density of a body is greater than the density of water, then the body will sink in water.
2. If the density of a body is lesser than the density of water, then the body will float on water.
3. The mass of water displaced by the body can be calculated as $m_w={\rho }_w\times V$, where $V$ is the volume of the body.

Step 3: Calculation of density of packet

The density of the packet can be calculated as, $\rho =\frac{m}{V}$

${\rho }_b=\frac{500}{350}=1.4285gc{m}^{-3}$

Since ${\rho }_b>{\rho }_w$, packet will sink in water.

Step 4: Calculation of mass of water displaced
Considering Archimedes Principle,

Mass of water displaced, $m_w={\rho }_w\times V$,

$m_w=1\times 350=350g$

Hence, the packet will sink in water, and the mass of water displaced will be $350g$.