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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids2 Marks
Question
Derive the condition of floatation of a body.
✓

Answer

When a body floats in a liquid with a part submerged in the liquid, the weight of the liquid displaced by the submerged part is always equal to the weight of the body. Let

V = volume of the body

$\sigma=$ density of its material

$\rho=$ density of the liquid in which the body floats such that its volume V' is outside the liquid.

Then volume of the body inside the liquid = V - V’

Weight of the displaced liquid $=(\text{V}-\text{V}')\rho\text{g}$

Also weight of the body $=\text{V}\sigma\text{ g}$

For the body to float,

Weight of the liquid displaced by the sumberged part = weight of the body,

i.e., $(\text{V}-\text{V}')\rho\text{g}=\text{V}\sigma\text{ g}$ or $\text{V}'=\frac{(\rho-\sigma)\text{V}}{\rho}$

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