An iron bar floats in mercury. What part of its volume is immersed in mercury.

An iron bar floats in mercury. What part of its volume is immersed in mercury. Iron density = 7800kg / m3; mercury = 13600kg / m3

ρzh = 7800 kg / m3.

ρр = 13600 kg / m3.

V / Vп -?

Since the iron bar floats in mercury, then, according to 1 Newton’s law, the action of forces on it is compensated. Only two forces act on the bar: gravity m * g directed vertically downward, buoyancy force of Archimedes Farch directed vertically upward.

Farch = m * g.

The force of Archimedes Farch is expressed by the formula: Farch = ρр * g * Vп.

We express the mass of an iron bar m by the formula: m = V * ρzh, where V is the volume of the entire iron bar, ρzh is the density of iron.

V * ρж * g = ρр * g * Vп.

V / Vп = ρр / ρl.

V / Vp = 13600 kg / m3 / 7800kg / m3 = 1.75 = 7/4.

Vp = 4 * V / 7.

Answer: the immersed volume of the iron bar is 4/7 of the total volume Vp = 4 * V / 7.