Lesson 6, Topic 1
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# Equilibrium of Bodies in Liquids

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It is a common experience that when an object is immersed in water, it becomes lighter whether it is wholly or partially immersed.

There is some upward force exerted by the liquid on an object when it is immersed in a fluid or liquid. This upward force experienced is called upthrust.

If the true weight of the object in air is W1 and the apparent weight in liquid is W2, then,

Upthrust, U = W1 – W2

Therefore the apparent weight when immersed in a liquid is;

W2 = W1 – U

Hence the apparent weight in liquid, W2, is less than the weight of the object in air, W1.

Upthrust depends on:

(i) Volume of an object immersed.
(ii) Density of the liquid into which it is immersed.

The magnitude of the upthrust is given by Archimedes’ principle.

Archimedes principle states that when a body is wholly or partially immersed in a fluid, it experiences an upthrust which is equal to the weight of the fluid displaced.

Upthrust, U = Vρg

= Vol. of object x density of liquid x acceleration due to gravity

If $$\frac{1}{3}$$ volume of the object is immersed in the liquid,

Then, U = $$\frac{V}{3}$$ x density of liquid x g

= $$\frac{V}{3}$$ρ g.

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