Two bodies of the same density, but different masses, float in the same liquid. The mass of the second

Two bodies of the same density, but different masses, float in the same liquid. The mass of the second body is 1.25 times the mass of the first body. The Archimedean force acts on the second body: 1) the same as on the first 2) to answer the question, you need to know the density of vitality 3) 1.25 times greater than the first 4) 1.25 times less than the first

Given:

ro1 = ro2 – the densities of bodies are the same;

m2 = 1.25 * m1 – the mass of the second body is 1.25 times the mass of the first body.

It is required to determine A2 – Archimedean force acting on the second body (in comparison with the first body).

According to the problem statement, two bodies float in the same fluid.

Then, the Archimedean force acts on the first body, equal to:

A1 = ro * g * V1 = ro * g * m1 / ro1, where ro is the density of the liquid, g is the acceleration of gravity.

The second body is acted upon by an Archimedean force equal to:

A2 = ro * g * V2 = ro * g * m2 / ro2.

Then:

A2 / A1 = (ro * g * m2 / ro2) / (ro * g * m1 / ro1) = ro * g * m2 * ro1 / (ro * g * m1 * ro2).

Since ro1 = ro2, we get:

A2 / A1 = m2 / m1 = 1.25 * m1 / m1 = 1.25, or

A2 = 1.25 * A1.

Answer: the second body is affected by 1.25 times greater Archimedean force than the first body (correct answer: 3).