Question

Explain Archimedes principle with an example.

Accepted Answer

Archimedes principle which states that "the upward force acting on a solid body which is partially or completely immersed in a fluid, is equal to the weight of the fluid displaced". This upward force is called buoyant force or upthrust.

We can observe the Archimedes principle by performing below experiment:

Consider a container filled water upto the level from where a pipe $P$ extends out. The other end of pipe $P$ opens to a small container $C_{2}$ placed on a weighing balance which measure $00.00$ [after the placement of the container $C_{2}$ ]. A block $B$ hangs on a spring balances $S$ which shows a reading of $7 kg$ .

(a) If we partially immerse the block in water we observe some water flows out from $C_{1} to C_{2}$ through $P$ . The weighing machine shows a reading $1 kg$ and the loss of reading in spring balance is $7 - 6 = 1 kg$ . This means that weight of water displaced by the block is equal to the loss in weight of block.

(b) Now, we completely immerse the block in water, we observe that the weight of water displaced by the block is $5 kg$ and the reading in spring balance is $2 kg$ . The loss of weight of block is $7 - 2 = 5 kg$ . Again we reach the same conclusion that the weight of water displaced by the block is equal to the loss in weight of the block.

(c) If the block is further immersed, no more water will be displaced by the block and therefore reading shown by weighing and spring balance remains unchanged.

The loss in weight of the block when the block is immersed in water is because of buoyant force acting vertically upwards. The loss in weight is equal to the buoyant force.

Conclusion 1: Buoyant force is directly proportional to volume of liquid displaced $(v)$ . If two bodies of different material have same volume, the buoyant force acting on them, when completely immersed in water, is same.

Instead of water if we take a liquid lighter than water then the volume displaced by the block on complete immersion will be the same but the buoyant force will be less. This is because the density of lighter liquid is less than that of water.

We know that,

$Density = \frac{Mass}{Volume} ∴ Mass = Density \times Volume$

For lighter liquids, the mass of the liquid displaced is less even when the volume displaced is the same.

Conclusion 2: Buoyant force directly proportional to the density of liquid

i.e., Buoyant force $α d$

It has also been found that buoyant force also depends on the acceleration due to gravity.

Conclusion 3: Buoyant force $α$ g

If we combine all the three, we get

Buoyant force $α V d g$

$\Rightarrow$ Buoyant force $α m g$

$\Rightarrow$ Buoyant force $α$ Weight of the liquid displaced

Sunil Batra Solutions for Chapter: Floating Bodies, Exercise 6: Summative Assessment

Sunil Batra Physics Solutions for Exercise - Sunil Batra Solutions for Chapter: Floating Bodies, Exercise 6: Summative Assessment

Questions from Sunil Batra Solutions for Chapter: Floating Bodies, Exercise 6: Summative Assessment with Hints & Solutions

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