There are two objects close to each other. If the mass of one of the objects is doubled while the distance remains the same, how does the gravitational force change? *
1 point
It becomes four times stronger
It becomes half as strong
It remains the same
It becomes twice as strong
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.
If the mass of one of the objects is doubled while the distance remains the same, the gravitational force will become twice as strong.
Therefore, the correct answer is: It becomes twice as strong.
To determine how the gravitational force changes when one object's mass is doubled while the distance remains the same, we need to apply Newton's law of gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers of mass:
F = G * (m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant
Now, let's examine the scenario. We have two objects close to each other, and the distance between them remains the same. If we double the mass of one object, it means that m1 is now twice its original value while m2 is unchanged. Plugging these values into the gravitational force equation:
F' = G * (2m2 * m2) / r^2
Simplifying this equation:
F' = 2 * (G * m2 * m2) / r^2
= 2 * F
This tells us that when the mass of one object is doubled while the distance remains the same, the gravitational force between them also doubles. Therefore, the correct answer is: "It becomes twice as strong."
The gravitational force between two objects can be calculated using the equation F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the objects.
In this case, if the mass of one of the objects is doubled while the distance remains the same, we can consider the mass of the other object as constant. Let's call the initial mass of the first object m1 and the initial mass of the second object m2.
When the mass of the first object is doubled, it becomes 2m1. The mass of the second object remains the same, so it remains as m2. The distance between the objects, denoted by r, remains unchanged.
Plugging these values into the equation for gravitational force, we get:
F_initial = G * (m1 * m2) / r^2
F_final = G * ((2m1) * m2) / r^2
To compare the two forces, we can take the ratio of the final force to the initial force:
F_final / F_initial = (G * ((2m1) * m2) / r^2) / (G * (m1 * m2) / r^2)
Canceling out common factors, we get:
F_final / F_initial = (2m1 * m2) / (m1 * m2)
The masses cancel out, resulting in:
F_final / F_initial = 2
Therefore, the gravitational force becomes twice as strong when the mass of one object is doubled while the distance remains the same.
The correct answer is: It becomes twice as strong.