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

Solution:

Given, mass of sealed packet, m = 500 g ;

volume, $\mathrm{V}=350 \mathrm{~cm}^{3} ;$ density, $\rho=?$

density of water, $\rho_{w}=1 \mathrm{~g} \mathrm{~cm}^{-3}$

Density $=\frac{\text { Mass }}{\text { Volume }}=\frac{500}{350}=1.428 \mathrm{~g} \mathrm{~cm}^{-3}$

The density of the packet is more than the density of water $\left(1 \mathrm{~g} \mathrm{~cm}^{-3}\right)$. Hence, the packet will sink in water. Thus, the volume of sealed packet (V) is equal to the volume of water displaced

$\left(\mathrm{V}_{\mathrm{w}}\right)$ as the packet is completely immersed in water.

i.e. $V_{w}=V=350 \mathrm{~cm}^{3}$

Now, mass of water displaced, $m_{w}=\rho_{w} \times V_{w}$

or $m_{w}=1 \times 350=350 \mathrm{~g}$

Thus, the mass of water displaced by the packet is $350 \mathrm{~g}$.
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