Question

The weight of an empty balloon on a spring balance is ${W_1}$. The weight becomes ${W_2}$ when the balloon is filled with air. Let the weight of the air itself be$\omega$. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of the air inside and outside the balloon.
A. ${W_2} = {W_1}$
B. ${W_2} = {W_1} + \omega$
C. ${W_2} < {W_1} + \omega$
D. ${W_2} > {W_1}$

Answer 1

Concept of upthrust or buoyancy and Archimedes principle as whenever a body is dispersed in a fluid it experiences buoyancy and there is some decrease in the real weight. Also air acts as fluid.
Apparent weight $=$ Real weight $-$ upthrust

Complete step by step answer:
$\to$ The upward force acting on a body immersed in a fluid is called upthrust or the buoyant force and this phenomenon is called buoyancy
$\to$ Archimedes principle states that when a body is partially or fully immersed in a fluid, it experiences an upthrust which is equal to the weight of the liquid or fluid displaced by it and its upthrust acts through the centre of gravity of the displaced fluid.
Now, initially the weight of balloon on spring balance $= {W_1}$
Weight of air filled $= W$
And weight of balloon after filling air on spring balance $= {W_2}$
Since, after filling air, the balloon attains a volume and an upthrust due to the outer air displacement acts on it as air is also a fluid so, ${W_2} =$apparent weight.
Now, we know that,
Apparent weight $=$ Real weight – upthrust
${W_2} =$real weight – upthrust ….. (i)
Real weight $=$ weight of empty balloon $+$ weight of air filled in it … (ii)
$= {W_1} + W$….. (ii)
Since, the pressure of air inside and outside the balloon is the same.
So, upthrust $=$ weight of air inside balloon
$= W$…. (iii)
So, from (i), (ii) and (iii), we get
${W_2} = \left( {{W_1} + W} \right) - W \\\ {W_2} = {W_1} \\\$
Or
${W_2} < {W_1} + W$

So, the correct answers are “Option A and C”.

Additional Information:
Some of the examples of buoyancy forces are:
$\bullet$ A cock taken inside water experiences an upthrust and comes to the surface.
$\bullet$ While drawing water from a well, a bucket is found too much lighter when it is inside water than when it comes outside
$\bullet$ Ice floats on water
$\bullet$A person can swim in sea water more easily than in river water as the density of seawater is more than the river water and so it exerts larger upthrust.

Note:
Liquids and gases both are considered as fluids and upthrust is found using Archimedes’ principle. This depends upon density outside and inside the body.