Question

A piece of copper having an internal cavity weighs \[264g\] in air and \[221g\] in water, Find the volume of the cavity. (Take density of copper is \[8.8g/cc\] )
(A) \[13cc\]
(B) \[14cc\]
(C) \[15cc\]
(D) \[16cc\]

Answer 1

Hint: We are asked to find the volume of the cavity given in the question. We use the principle of Archimedes principle. We can start by finding the volume of copper. Then we can find the buoyant force by equating it to the change in weight. Then the volume of water displaced is found. Finally, we get the required solution by subtracting the volume of copper from the total volume found.
Formulas used: The formula used to find the volume from the density of a given material is, \[V = \dfrac{w}{D}\]
Where \[M\] is the mass of the material
\[D\] is the density of the material.
The volume of the cavity is, \[{V_{cavity}} = {V_{total}} - {V_{copper}}\]

Complete answer:
We can start by noting down the given data from the question
The weight of the piece of copper in air is given as, \[{w_{air}} = 264g\]
The weight of the piece of copper in water is given as, \[{w_{water}} = 221g\]
The density of copper is given as, \[{D_{Cu}} = 8.8g/cc\]
We can move onto finding the volume of the given piece of copper in air,
\[{V_{air}} = \dfrac{{{w_{air}}}}{D} \Rightarrow \dfrac{{264}}{{8.8}} = 30cc\]
Now that we have found the value of volume of the piece of copper in air, we can move onto finding the value of change in weight of the piece of copper, \[\Delta w = {w_{air}} - {w_{water}} = 264 - 221 = 43g\]
We can use this value of weight to find the value of water displaced by using the formula, \[V = \dfrac{w}{D}\]
Substituting, we get \[V = \dfrac{w}{D} = \dfrac{{43}}{1} = 43cc\]
This is the total volume of the copper piece. Now in order to find the volume of the material, we subtract the volume in air from the total volume of water displaced
That is, \[{V_{cavity}} = {V_{total}} - {V_{Cu}} \Rightarrow 43 - 30 \Rightarrow 13cc\]
In conclusion, the right answer is option (A) \[13cc\].

Note:
Archimedes' principle, physical law of buoyancy, discovered by the ancient Greek mathematician and inventor Archimedes, stating that a body that is completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force, the magnitude of which is equal to the weight of the fluid displaced by the body.