Question

State Archimedes' principle and describe an experiment to verify it.

Answer 1

Part 1: Definition,
Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid.

Part 2: Experiment to verify Archimedes' principle,

Apparatus: Metal solid piece, thread, hook, eureka can, measuring cylinder, and spring balance.

Procedure:

1. Suspend a solid by a thin thread from the hook of a spring balance. Note its weight.
2. Now take a eureka can and fill it with water to its spout. Arrange a measuring cylinder below the spout of the eureka can.
3. Now, immerse the solid gently into the water of the eureka can. The water displaced by it gets collected in the measuring cylinder, as shown in the figure. When water stops dripping through the spout, note the weight of the solid and the volume of water collected in the measuring cylinder.

Observation:

1. As shown in the figure, the solid weighs $300gf$in air and $200gf$when it is completely immersed in water.
2. The volume of water collected in the measuring cylinder is $100ml$ or $100c{m}^3$.

Conclusion:

1. The loss in weight = $300gf-200gf=100gf$ [Equation 1]
2. Volume of water displaced = Volume of solid = $100c{m}^3$
   Since, density of water = $1g/c{m}^3$
   Therefore, $Weightofwaterdisplaced=Densityofwater\times Volumeofwater=100gf$ [Equation 2]
3. From eqns. (i) and (ii)
   Weight of water displaced = Upthrust or loss in weight.
   Thus, the weight of water displaced by a solid is equal to the loss in weight of the solid.
4. This verifies Archimedes' principle.