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.
The gravitational force between two objects is given by 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 objects, and r is the distance between the objects.
In this scenario, if the mass of one of the objects is doubled while the distance remains the same, we can substitute the new mass into the equation:
F' = (G * (2m1) * m2) / r^2
By simplifying the equation, we get:
F' = (2 * F)
Therefore, the gravitational force 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 the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, the distance (r) remains the same. Let's consider the scenario where the mass of m1, one of the objects, is doubled. We have:
F1 = (G * (2m) * m) / r^2
F2 = (G * m * m) / r^2
To find how the gravitational force changes, we can compare F1 to F2. We can simplify the formula by canceling out common terms:
F1/F2 = ((2m) * m) / (m * m)
F1/F2 = 2
Comparing F1 to F2, we can see that F1 is twice as strong as F2. Therefore, the gravitational force becomes twice as strong when the mass of one object is doubled while the distance remains the same.
So, the correct answer is: "It becomes twice as strong."