Question

a student is trying to find a direct proportionality rule between the mass of an object. she tested four objects, each with a different volume and mass. the table below shows the data she collected. she noticed that, as the volume of the object increases, the mass of the object also increases. she wants to prove that the mass of an object is directly proportional to the volume of the object. which of the following procedures should she perform?
based on the data in the table, which law allows us to conclude that the
a. increase the length of the object
b. decrease the number of trials
c. determine the relationship between mass (m) and volume (v)
d. keep the number of trials constant

Explanation:

Step1: Analyze the relationship between mass and volume

According to Archimedes' principle, the buoyant force \(F_b=
ho_{fluid}gV_{displaced}\). When the object is floating, \(F_b = mg\) (where \(m\) is the mass of the object). So \(
ho_{fluid}gV_{displaced}=mg\), and \(V_{displaced}=\frac{m}{
ho_{fluid}}\).

Step2: Consider the change in mass

If the mass \(m\) of the object increases (assuming the density of the fluid \(
ho_{fluid}\) is constant), from \(V_{displaced}=\frac{m}{
ho_{fluid}}\), we can see that \(V_{displaced}\) (the volume of water displaced, which is related to the number of tubes submerged) will increase.

Answer:

Increase the number of tubes submerged.