How many times is the density of a body greater than the density of a liquid if the body falls

How many times is the density of a body greater than the density of a liquid if the body falls in it with an acceleration of 8m / s?

Given:

a = 8 m / s ^ 2 – the acceleration with which the body falls in the liquid;

ro1 – body density;

ro2 is the density of the liquid;

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

V is the volume of the body.

It is required to determine ro1 / ro2, how many times the density of the body is higher than the density of the liquid.

The body is affected by the downward gravity and the upward Archimedean force. Then, according to Newton’s second law:

F gravity – Farkhimedova = m * a, where m is body mass.

m * g – V * ro2 * g = m * a;

ro1 * V * g – ro2 * V * g = ro1 * V * a;

ro1 * V * g – ro1 * V * a = ro2 * V * g;

ro1 * g – ro1 * a = ro2 * g;

ro1 * (g – a) = ro2 * g;

ro1 / ro2 = g / (g – a) = 10 / (10 – 8) = 10/2 = 5 times.

Answer: the density of the body is 5 times greater than the density of the liquid.