Question

which of the following statements about the effects of gravity are true?
select all that apply
a you and your desk attract each other with the same force of gravity as earth attracts you.
b objects that are closer together have a weaker force of gravity between them.
c the force of gravity is greater between the moon and the sun than between the moon and earth.
d objects with greater mass have a stronger force of gravity between them.
e the moon circles around earth rather than the sun because the force of gravity is greater between the moon and earth.

Explanation:

• Option a: According to Newton's third law of motion (action - reaction), the gravitational force between two objects is mutual. The force with which you attract the Earth is equal in magnitude to the force with which the Earth attracts you. Similarly, the force between you and your desk is much smaller than the force between you and the Earth because the mass of the Earth is much larger than the mass of the desk. So, this statement is false.
• Option b: The gravitational force formula is \(F = G\frac{m_1m_2}{r^{2}}\), where \(G\) 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. As \(r\) decreases (objects are closer), the gravitational force \(F\) increases. So, this statement is false.
• Option c: The gravitational force formula \(F = G\frac{m_1m_2}{r^{2}}\). The mass of the Sun (\(m_{sun}\approx1.989\times 10^{30}\space kg\)), the mass of the Earth (\(m_{earth}\approx5.972\times 10^{24}\space kg\)), and the mass of the Moon (\(m_{moon}\approx7.348\times 10^{22}\space kg\)). The distance between the Moon and the Earth (\(r_{moon - earth}\approx3.844\times 10^{8}\space m\)) and the distance between the Moon and the Sun (\(r_{moon - sun}\approx1.5\times 10^{11}\space m\)). Using \(F = G\frac{m_1m_2}{r^{2}}\), we find that \(F_{moon - earth}>F_{moon - sun}\) because the effect of the much smaller \(r\) (distance) between the Moon and the Earth outweighs the larger mass of the Sun. So, this statement is false.
• Option d: From the formula \(F = G\frac{m_1m_2}{r^{2}}\), if \(r\) is constant, as \(m_1\) and \(m_2\) increase (objects have greater mass), the gravitational force \(F\) increases. So, this statement is true.
• Option e: As calculated using \(F = G\frac{m_1m_2}{r^{2}}\), the gravitational force between the Moon and the Earth is greater than the gravitational force between the Moon and the Sun (because of the much smaller distance between the Moon and the Earth). So, the Moon circles around the Earth, and this statement is true.

Answer:

d. Objects with greater mass have a stronger force of gravity between them.
e. The moon circles around Earth rather than the sun because the force of gravity is greater between the moon and Earth.