Sure, let's go through the choices to determine which one correctly describes the relationship between mass and gravitational force:
1. Choice (a): "Smaller distance results in greater force."
- This statement concerns the distance between the objects, not the mass. It's true that the force increases as the distance decreases, but this does not answer the question related specifically to mass.
2. Choice (b): "Smaller mass results in greater force."
- This statement is incorrect. According to the law of universal gravitation, the gravitational force is directly proportional to the product of the two masses. Therefore, smaller mass will result in smaller force, not greater.
3. Choice (c): "Greater distance results in smaller force."
- Similar to choice (a), this statement concerns the distance between the objects. It is true that the gravitational force decreases as the distance increases, but again, this does not directly answer the question about mass.
4. Choice (d): "Greater mass results in greater force."
- This statement accurately describes the relationship between mass and gravitational force. According to the law of universal gravitation, the force of attraction between two objects is directly proportional to the product of their masses. Hence, if one or both of the masses increase, the gravitational force also increases.
So, the correct answer to the question regarding the relationship between mass and gravitational force is:
(d) Greater mass results in greater force.
For future reference, remember that the gravitational force [tex]\( F \)[/tex] between two objects of masses [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex], separated by a distance [tex]\( r \)[/tex], is given by the formula:
[tex]\[ F = G \frac{m_1 m_2}{r^2} \][/tex]
where [tex]\( G \)[/tex] is the gravitational constant. This formula shows that the gravitational force is directly proportional to the masses [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex].
