Question

if two objects each have a mass of 10 kg, then the force of gravity between them __________. a is greater when they are closer together b is the same no matter how close they are together c is 100 kg d depends only on their masses

Explanation:

According to Newton's law of universal gravitation, \(F = G\frac{m_1m_2}{r^2}\), where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between their centers of mass. When \(m_1 = m_2=10\space kg\) (constant masses), \(F\) is inversely proportional to \(r^2\). So, as \(r\) (distance) decreases, \(F\) (gravitational force) increases.

• Option a: Since \(F\propto\frac{1}{r^2}\) (with \(m_1\) and \(m_2\) constant), when \(r\) is smaller (closer together), \(F\) is larger. This is correct.
• Option b: \(F\) changes with \(r\) (from \(F = G\frac{m_1m_2}{r^2}\)), so it is not the same no matter the distance. This is incorrect.
• Option c: \(F\) has the unit of force (Newton, \(N\)), while \(kg\) is the unit of mass. This is incorrect.
• Option d: \(F\) depends on both masses (\(m_1\) and \(m_2\)) and the distance (\(r\)) between them (\(F = G\frac{m_1m_2}{r^2}\)), not only on masses. This is incorrect.

Answer:

A. is greater when they are closer together