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?
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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. This is because doubling the mass of one object while keeping the distance constant will directly double the product of their masses, resulting in a doubled gravitational force.
Therefore, the correct answer is: It becomes twice as strong.
The gravitational force between two objects is given by the formula 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 centers of the objects.
If the mass of one of the objects is doubled while the distance remains the same, let's consider the object with the doubled mass as object 1 and the other object as object 2.
Now, let's analyze the change in gravitational force:
1. The mass of object 1 is doubled, so m1 becomes 2m2.
2. The distance between the objects, r, remains the same.
3. Plugging in the new values into the equation, we have F_new = G * ((2m2) * m2) / r^2.
Simplifying the equation, we have F_new = G * (2 * m2^2) / r^2.
Comparing F_new to the original gravitational force, F, we can conclude that the gravitational force becomes four times stronger. Therefore, the correct answer is: It becomes four times stronger.
To determine how the gravitational force changes when the mass of one object is doubled while the distance remains the same, we can use 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 their centers.
Let's assume the initial force between the two objects is F.
When the mass of one object is doubled, it means its mass becomes 2m, where m is the initial mass.
Using Newton's law of universal gravitation, we can calculate the new force, F'.
F' = G * (2m) * m / r^2
= 2 * (G * m^2 / r^2)
= 2F
Therefore, doubling the mass of one object while keeping the distance the same causes the gravitational force to become twice as strong (option D).