The metal ball floats half submerged in mercury. What is the density of the ball?

Given:

ro1 = 13.6 g / cm ^ 3 = 13600 kg / m ^ 3 – the density of mercury;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the density of the ball ro2 (kg / m ^ 3).

According to Archimedes’ law, a body immersed in a liquid displaces a volume of liquid equal to its volume. Since, according to the condition of the problem, the ball floats half submerged, then:

F gravity = Farchimedes;

m * g = ro1 * g * V / 2;

m * g = ro1 * g * m / (2 * ro2);

1 = ro1 / (2 * ro2);

ro2 = ro1 / 2 = 13600/2 = 6800 kg / m ^ 3.

Answer: the density of the ball is 6800 kg / m ^ 3 (6.8 g / cm ^ 3).