Question

select the correction relationship between distance of objects, mass, and the force of gravity.
this diagram describes the mechanisms of
newtons law of universal gravitation; a
point mass ( m_1 ) attracts another point mass
( m_2 ) by a force ( f_2 ). the force is proportional
to the product of the two masses and
inversely proportional to the square of the
distance (r) between the point masses.
as the distance between objects increases, gravitational force ____.
as the mass of an object increases, gravitational force____.

Explanation:

Step1: Analyze the relationship between distance and gravitational force

According to the formula \(F = G\frac{m_1m_2}{r^2}\), when \(m_1\) and \(m_2\) are constant, if \(r\) (distance) increases, since \(F\) is inversely proportional to \(r^2\) (\(F\propto\frac{1}{r^2}\)), \(F\) (gravitational force) will decrease.

Step2: Analyze the relationship between mass and gravitational force

According to the formula \(F = G\frac{m_1m_2}{r^2}\), when \(r\) is constant, if \(m_1\) or \(m_2\) (mass) increases, since \(F\) is proportional to \(m_1m_2\) (\(F\propto m_1m_2\)), \(F\) (gravitational force) will increase.

Answer:

As the distance between objects increases, gravitational force \(decreases\).
As the mass of an object increases, gravitational force \(increases\).