A copper ball with an internal cavity weighs 2.59 N in air and 2.17 N in water. Find the volume of the internal cavity of the ball.

Given:
P1 = 2.59 Newton – the weight of the copper ball in the air;
P2 = 2.17 Newton is the weight of a copper ball in water;
ro = 8900 kg / m3 (kilogram per cubic meter) – copper density;
ro1 = 1000 kg / m3 – water density;
g = 10 N / kg (Newton / kilogram) – acceleration of gravity.
It is required to determine V (m3) – the volume of the inner cavity of the ball.
Let’s find the mass of the ball:
m = P1 / g = 2.59 / 10 = 0.259 kilograms.
Let’s find the value of the Archimedean force acting on the ball:
A = P1 – P2 = 2.59 – 2.17 = 0.42 Newton.
Then the actual volume of the ball will be:
V2 = A / (ro1 * g) = 0.42 / (1000 * 10) = 0.42 * 10-4 = 4.2 * 10-5 m3.
Let us find the volume that the copper ball would occupy if there was no cavity in it:
V1 = m / ro = 0.259 / 8900 = 2.9 * 10-5 m3.
Then the volume of the cavity is:
V = V1 – V2 = 4.2 * 10-5 – 2.9 * 10-5 = 1.3 * 10-5 m3.
Answer: the volume of the inner cavity of the copper ball is 1.3 * 10-5 m3.