Tamil Nadu Board of Secondary EducationHSC Science Class 11

# State and prove Archimedes principle. - Physics

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Long Answer

State and prove Archimedes principle.

#### Solution

Archimedes principle

Archimedes principle states that when a body is partially or wholly immersed in a fluid, it experiences an upward thrust equal to the weight of the fluid displaced by it, and its upthrust acts through the center of gravity of the liquid displaced.

Proof: Consider a body of height h lying inside a liquid of density p, at a depth x below the free surface of the liquid. The area of a cross-section of the body is a. The forces on the sides of the body cancel out.

Buoyant force on a body

Pressure at the upper face of the body,

P1 = xρg

Pressure at the lower face of the body,

P2 = (x + h)pρg

Thrust acting on the upper face of the body is F1 = P1a = xρga acting vertically downwards.

Thrust acting on the lower face of the body is F2 = P2a = (x+h)ρga acting vertically upwards.

The resultant force (F2 – F1) is acting on the body in the upward direction and is called Upthrust (U).

∴ U = F2 – F1 = (x + h)ρg – xρga = ahρg

But, ah = V, the volume of the body = volume of liquid displaced.

U = Vρg = Mg

[∴ M = Vρ = mass of liquid displaced]

i.e., upthrust or buoyant force = Weight of liquid displaced.

This proves the Archimedes principle.

Concept: Fluids
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Chapter 7: Properties of Matter - Evaluation [Page 92]

#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Physics Volume 1 and 2 Answers Guide
Chapter 7 Properties of Matter
Evaluation | Q III. 6. | Page 92
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