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. Therefore, if the mass of one of the objects is doubled while the distance remains the same, the gravitational force between them becomes twice as strong. So the correct answer is "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 their centers. In this case, if the mass of one object is doubled while the distance remains the same, we can analyze the effect on the gravitational force.
Let's consider the initial gravitational force between the objects as F1, and the final gravitational force after doubling the mass as F2.
According to the formula F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers, we see that the only change is in the mass of one object.
Now, let's compare the initial and final gravitational forces step by step:
1. Initial force: F1 = (G * m1 * m2) / r^2
2. Final force: F2 = (G * (2 * m1) * m2) / r^2
Simplifying the equation, we get:
F2 = (G * 2 * m1 * m2) / r^2
Notice that 2 * m1 is equivalent to doubling the mass of object 1.
So, when the mass of one of the objects is doubled while the distance remains the same, the gravitational force becomes twice as strong. Therefore, the correct answer is: "It becomes twice as strong."
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.
Newton's law of universal gravitation states that 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.
Mathematically, it can be represented as:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 N.m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the objects.
In this scenario, we have two objects close to each other, and we are doubling the mass of one object while keeping the distance unchanged.
Let's assume the initial mass of both objects is m and the distance between them is r.
When we double the mass of one object, its new mass will be 2m, while the mass of the other object remains m.
Now, let's calculate the ratio of the gravitational forces F2 (after doubling the mass) to F1 (initial force) using the formula:
F2/F1 = ((G * m * 2m) / r^2) / ((G * m * m) / r^2)
Simplifying and canceling out common factors, we get:
F2/F1 = (2m * m) / (m * m)
F2/F1 = 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.