Question

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

Short answer

The fraction of iron in mercury is 0.57.

Step-by-step solution

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.

Calculation the fraction of the iron

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

F_B = V_inρg

Here, ρ_f = 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 = Vρ_sg

Here, ρ_s = 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.