Question

A spring balance measures the weight of an object in air to be \[0.1N\]. It shows a reading of \[0.08N\] when the object is completely immersed in water. If the value of acceleration due to gravity is $10m/s^{2}$, the volume of the object is
\[\begin{align}
  & A.20c{{m}^{3}} \\
 & B.80c{{m}^{3}} \\
 & C.200c{{m}^{3}} \\
 & D.2c{{m}^{3}} \\
\end{align}\]

Answer 1

Hint: We know that when an object is immersed in a liquid, it experiences an upward thrust or force called the buoyant force. This property or nature of liquids is called buoyancy. This is caused due to the difference in the pressure above and inside liquid.

Formula used:
$F_{b}=W$

Complete step-by-step answer:
Here, it is given that the spring balance measures a force of $F_{a}=0.1N$ and the same when immersed in the water shows a reading $F_{w}=0.08N$
Then the difference in the forces gives the force due to buoyancy $F_{b}=F_{a}-F_{b}=0.1-0.08=0.02N$
From Archimedes principle, we know that the buoyant force is equal to the weight of the fluid displaced.
But we need to find the volume of the object. We know that density is a constant and it is the ratio between the mass and volume of the substance. Here since the liquid is water, we know that the density of the water is $10^{3}cm^{3}$ and if $V$ is the volume of the water displaced, we can write the mass of the water displaced as $M=V\times 10^{3}$ then the weight of the water displace is given as $W=V\times 10^{3}\times 10=V\times 10^{4}$.
Then from Archimedes principle $F_{b}=W$
$\implies V\times 10^{4}=0.02$.
$\implies V=\dfrac{0.02}{10^{4}}=2cm^{3}$
Thus the volume of water displaced is $2cm^{3}$
Hence the answer is \[D.2c{{m}^{3}}\]

So, the correct answer is “Option D”.

Additional Information: Archimedes principle and buoyancy are two important properties which are often used in fluid mechanics.
 Buoyancy has wide applications like the designing of submarines, aeroplanes. It is also used by birds and fish to move through the water and air respectively.

Note: Mass is a property of the substance, whereas weight is the force due to gravity acting on the body with some mass. Also, Archimedes principle and buoyancy are properties of liquids and can be extended to fluids as well.