Suppose the mass of each of two spherical objects is doubled, and the distance between their centers is three times as large. How is the magnitude of the force of gravity between them affected?
(Points : 5)
It is 4/9 as large.
It is 4/3 as large.
It is 2/9 as large.
It is 3/2 as large.
It is 2/3 as large.
initially, F = Gmm/r^2
later, we have G(2m)(2m)/(3r)^2 = 4/9 F
3/2
The force of gravity 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 call the initial mass of each object "m" and the initial distance between their centers "d".
When the mass of each object is doubled, the new mass of each object becomes "2m".
When the distance between their centers is three times as large, the new distance becomes "3d".
Using the formula for the force of gravity:
F = G * (m1 * m2) / (d^2)
where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between their centers.
If we plug in the new values, the formula becomes:
F' = G * (2m * 2m) / (3d)^2 = G * (4m^2) / (9d^2)
Comparing F and F', we can see that the new force F' is (4/9) times as large as the initial force F.
Therefore, the magnitude of the force of gravity between the two objects is 4/9 as large.
To determine how the magnitude of the force of gravity between two objects is affected when their masses and distances change, we can use the equation for the force of gravity:
F = G * (m1 * m2) / r^2
Where:
F is the force of gravity between the objects
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between their centers
In this case, the mass of each object is doubled, and the distance between their centers is three times as large. Let's call the original mass of each object "m" and the original distance between their centers "r". Therefore, the new mass will be 2m, and the new distance will be 3r.
Now, we can calculate the new force of gravity (F') using the equation:
F' = G * (2m * 2m) / (3r)^2
Simplifying this expression, we get:
F' = G * (4m^2) / (9r^2)
Comparing this expression to the original equation, we can see that the new force of gravity is:
4/9 times as large as the original force of gravity.
Therefore, the correct answer is: It is 4/9 as large.