The mass of an object doubles. What happens to the gravitational force between it and another object, assuming they remain the same distance apart? *
1 point
a. The amount of the gravitational force decreases by one-half.
b. The amount of the gravitational force quadruples.
c. The amount of the gravitational force doubles.
d. The amount of the gravitational force remains the same.
c. The amount of the gravitational force doubles.
To determine what happens to the gravitational force between two objects when the mass of one object doubles, we can refer to Newton's law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, the formula for gravitational force (F) is given by:
F = G * (m1 * m2) / r^2
Where:
- G is the gravitational constant
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
Now, let's consider the scenario where the mass of one object doubles while the other remains the same distance apart. Let's assume the mass of the first object is m1 and the mass of the second object is m2.
Initially, the gravitational force between the two objects is:
F_initial = G * (m1 * m2) / r^2
Now, if the mass of the first object doubles, its new mass becomes 2m1. The gravitational force after doubling the mass becomes:
F_new = G * ((2m1) * m2) / r^2
We can simplify this expression by cancelled out common terms:
F_new = 2 * (G * (m1 * m2) / r^2)
We can see that the new gravitational force is twice the initial gravitational force. Therefore, the correct answer is:
c. The amount of gravitational force doubles.
To summarize, when the mass of an object doubles while the distance remains the same, the gravitational force between the object and another object will double as well.