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Chapter 10: Q23P (page 260)

(II) What fraction of iron will be submerged when it floats in mercury?

Short Answer

Expert verified

The fraction of iron in mercury is 0.57.

Step by step solution

01

Understanding the floatation of a solid

For equilibrium, during floatation, the weight of the substance will be equal to the buoyant force of the fluid.

02

Calculation the fraction of the iron

The buoyant force due to the Vin part of the iron inside mercury is,

FB = Vinρg

Here, ρf = 13.6 x 103 kg/m3 is the density of the mercury, and g is the gravitational acceleration.

The weight of iron of volume V is,

W = Vρsg

Here, ρs = 7.8 x 103 Kg/m3 is the density of the iron.

Equate these two forces for equilibrium and get,

Substitute the given values and get,

Hence, the submerged fraction of iron is 0.57.

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