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

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Given:
The volume of a $500\ g$ sealed packet is $350\ cm^3$.

To do:
$(i)$. To check whether the packet will float or sink in water if the density of water is $1\ g cm^{-3}$.
$(ii)$. To calculate the mass of the water displaced by this packet

Solution:
To check whether the packet will float or sink, we will have to compare the densities of the sealed packet and the water. If the density of the sealed packet is less than that of the water$(1\ g cm^{-3})$, then the sealed packet will float. If the density of the sealed packet is greater than that of the water$(1\ g cm^{-3})$, then the sealed packet will sink. let us find the density of the sealed packet first and then compare it with that of water:

Density of the sealed packet:

As given, the volume of sealed packet $=500\ g$

Mass of sealed packet $=350\ cm^3$

Density of sealed packet, $\rho=\frac{500}{350}=1.42\ g/cm^3$

Comparison of densities:

On comparing the densities of the sealed packet and water.

$1.42\ g/cm^3$ > $1\ g cm^{-3}$

Here the density of the sealed packet is greater than the density of the water. So, the sealed packet will sink.

Mass of the displaced water:

Considering Archimedes Principle,

Displaced water volume$=$Force exerted on the sealed packet.

The volume of water displaced$=350\ cm^3$

Therefore displaced water mass$=\rho\times V$

$=1\times 350$

Mass of displaced water$=350\ g$

Conclusion:
From the above calculations, we can conclude that the packet will sink. The mass of the water displaced by this packet is $350\ g$.
Updated on 10-Oct-2022 13:22:47