A piece of metal weighing m = 0.78 kg has a weight P1 = 6.8 N in water, and P2 = 7.1 N. in a certain liquid.

A piece of metal weighing m = 0.78 kg has a weight P1 = 6.8 N in water, and P2 = 7.1 N. in a certain liquid. Determine the density of the liquid.

It is known from the condition that a piece of metal weighing m = 0.78 kg has a weight P1 = 6.8 N in water, and P2 = 7.1 N. In a certain liquid, it is necessary to determine the density of the liquid.
Let’s start with a short entry given:
m = 0.78 kg;
P1 = 6.8 H;
P2 = 7 H;
P3 = 7.1 H,
To find:
p2, p3 -?
Decision:
Let’s remember what forces act on the body in water:
1. The force of Archimedes, directed upward;
2. Downward gravity.
Let’s write down the body weight in water as a formula:
mg – p1gV = P1;
Where p1 is the density of water and V is the volume of the body.
Let’s express the volume of the body:
V = (mg – P1) / pg.
Let’s write the formulas for the second liquid:
mg – p2gV = P2;
p2 = (mg – P2) / gV = (mg – P2) * p1 / (mg – P1).
p3 = (mg – P3) / gV = (mg – P3) * p1 / (mg – P1).