A solid homogeneous body, immersed in a liquid with density ro1, weighs P1. And in a liquid with a density

A solid homogeneous body, immersed in a liquid with density ro1, weighs P1. And in a liquid with a density of ro2, P2 weighs. Determine the density of the body substance.

Given:

ro1 is the density of the first liquid;

P1 is the weight of the body immersed in the first liquid;

ro2 is the density of the second liquid;

P2 is the weight of the body immersed in the second liquid.

It is required to find the density of the body matter ro.

Path m and V – body mass and volume. Then, when the body is immersed in the first liquid:

Ft – Fа = P1 – where Ft is the force of gravity acting on the body, Fа is the buoyant (Archimedean) force.

m * g – ro1 * g * V = P1, or given that V = m / ro:

m * g – ro1 * g * m / ro = P1

m * g (1 – ro1 / ro) = P1

When the body is immersed in the second fluid, we obtain a similar equation:

m * g (1 – ro2 / ro) = P2.

Let’s divide the first equation by the second:

m * g (1 – ro1 / ro) / m * g (1 – ro2 / ro) = P1 / P2

(1 – ro1 / ro) / (1 – ro2 / ro) = P1 / P2

P2 * (1 – ro1 / ro) = P1 * (1 – ro2 / ro)

P2 * ro – P2 * ro1 = P1 * ro – P1 * ro2

P2 * ro – P1 * ro = P2 * ro1 – P1 * ro2, hence

ro = (P2 * ro1 – P1 * ro2) / (P2 – P1).

Answer: the density of matter is ro = (P2 * ro1 – P1 * ro2) / (P2 – P1)