Question

1. the strength of gravity between two objects is directly proportional to: a) the square of their distance b) the sum of their masses c) the product of their masses d) their speeds

Explanation:

To solve this, we recall Newton's law of universal gravitation, which is given by the formula \( F = G\frac{m_1m_2}{r^2} \), 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. From this formula, we can see the relationship between the gravitational force (strength of gravity) and other quantities:

• Option A: The formula shows that \( F \) is inversely proportional to the square of the distance (\( r^2 \)), not directly proportional. So A is incorrect.
• Option B: The formula involves the product of the masses (\( m_1m_2 \)), not the sum. So B is incorrect.
• Option C: From \( F = G\frac{m_1m_2}{r^2} \), we can see that \( F \) is directly proportional to the product of the masses (\( m_1m_2 \)) (since \( G \) and \( r^2 \) are constants in the proportionality relationship when considering how \( F \) depends on masses). So C is correct.
• Option D: The formula for gravitational force does not involve the speeds of the objects at all. So D is incorrect.

Answer:

C) The product of their masses