Question

the table provided shows data collected during an experiment. which of the following claims is supported by the data?
gravitational forces are proportional to the masses of the two objects.
gravitational forces are strongest between objects with identical masses.
gravitational forces are weakest when one object is more massive than the other.
gravitational forces can never exceed an upper limit, regardless of the masses.

Explanation:

Step1: Analyze the relationship between mass and gravitational force

According to Newton's law of universal gravitation \(F = G\frac{m_1m_2}{r^2}\) (assuming the distance \(r\) is constant in this experiment), when \(G\) and \(r\) are fixed, \(F\) is proportional to \(m_1m_2\). Looking at the data in the table, as the sum (or product, since we are comparing trends) of the masses of the two objects (\(m_1 + m_2\) or \(m_1\times m_2\), and here we can simply observe the trend of mass combination and force) increases, the gravitational force \(F\) increases. For example, when the masses are \(54 + 67=121\) (approximate combination for trend - looking, actual formula is \(F = G\frac{m_1m_2}{r^2}\)), the force is \(190\); when masses are \(187+194 = 381\), the force is \(500\). This shows a positive - correlation (proportional - like) relationship between the masses of the two objects and the gravitational force.

Step2: Eliminate other options

• Option 1: There is no indication in the data that gravitational forces have an upper limit regardless of mass.
• Option 2: The data does not support the claim that gravitational forces are weakest when one object is more massive. In fact, when masses are larger (in combination, considering the formula \(F = G\frac{m_1m_2}{r^2}\)), the force is larger.
• Option 3: The data is about two objects with different masses (not identical masses).

Answer:

Gravitational forces are proportional to the masses of the two objects.