A body in a liquid moves uniformly upward with an acceleration of 2 m / s. the density of the body

A body in a liquid moves uniformly upward with an acceleration of 2 m / s  the density of the body substance is 700 kg / m3. find the density of the liquid. disregard fluid resistance.

Given:

a = 2 m / s ^ 2 – the acceleration with which the body moves in the fluid;

ro = 700 kg / m ^ 3 is the density of the body substance;

g = 9.8 m / s ^ 2 – acceleration of gravity.

It is required to find the density of the liquid ro1.

Since, according to the condition of the problem, the body moves upward, then according to Newton’s second law:

Fа – Fт = m * a – where Fа – Archimedean force, Fт – gravity, m – body mass

ro1 * V * g – m * g = m * a

ro1 * m * g / ro – m * g = m * a

ro1 * g / ro – g = a

ro1 * g = (a + g) * ro

ro1 = (a + g) * ro / g = (2 + 9.8) * 700 / 9.8 = 842.9 kg / m ^ 3.

Answer: the density of the liquid is 842.9 kg / m ^ 3.