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

Hint: Here we will be applying a concept of Archimedes principle and floatation of a body. Archimedes principle states that when a body is immersed fully or partially in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it.

Complete step-by-step answer:
Given, the volume of sealed package, ${{\text{V}}_{{\text{pack}}}} = 350c{m^3}$
Mass of the sealed pack ${M_{pack}} = 500g$
Density of water, ${\rho _{water}} = 1gc{m^{ - 3}}$
Now, we will find, density of the sealed pack,
${\rho _{pack}} = \dfrac{{mass{\text{ }}of{\text{ }}the{\text{ }}pack}}{{volume{\text{ }}of{\text{ }}the{\text{ }}pack}}$
${\rho _{pack}} = \dfrac{{500}}{{350}}$
$ = 1.428gc{m^{ - 3}}$
From this we can say, the density of sealed packs is more compared to the density of water.
Therefore, the packet will sink.
Then, the mass of the water displaced by this packet$ = {V_{pack}} \times {\rho _{water}}$
$m = 350 \times 1 = 350g$
Thus, the mass of the water displaced by this packet is 350g.

Additional information:
When a solid body is immersed in a liquid the net upward thrust (buoyant force) on it is equal to the weight of the liquid displaced by the body. When the solid body immersed in a liquid is released, (i) it moves downwards (sinks) if the weight W of the body is greater than the resultant up thrust R on it $\left( {W > R} \right)$ (ii) it moves upwards towards the surface if the weight W of the body is less than the resultant upthrust R on it $\left( {W < R} \right)$ and (iii) the body remains at the same position in equilibrium if its weight W is equal to the resultant up thrust R on it $\left( {W = R} \right)$.
According to Archimedes’s principle, when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.
The loss of weight of the body is equal to the resultant upthrust. The resultant upthrust on a body is called buoyancy. The resultant upthrust acting on a body is equal to the weight of the displaced liquid.
Archimedes principle has many applications. It is used in designing ships and submarines. Lactometers, which are used to determine the purity of a sample of milk and hydrometers used for determining density of the liquids.

Note: In this type of question, comparing the density of the substance is important to write whether the given body will sink or float. If the density of the object is more than that of water then the object will sink.
If the density of the object is less than that of water then the object will float.