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The gravitational force between two objects each of mass m, separated by a distance r, is F. Gravitational force between two objects each of mass 2m separated by a distance 2r, will be
- a)F
- b)F/2
- c)2F
- d)4F
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The gravitational force between two objects each of mass m, separated ...
Gravitational Force between Two Objects
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 two objects
- r is the distance between the centers of the two objects
Given Parameters
In this problem, we are given the following parameters:
- Two objects with mass m each
- Separated by a distance r
Calculating the Gravitational Force
Let's calculate the gravitational force between the two objects using the given parameters:
F = G * (m * m) / r^2
Increasing the Mass and Distance
Now, let's consider the scenario where the masses of the two objects are doubled and the distance between them is also doubled:
- Mass of each object = 2m
- Distance between the objects = 2r
Calculating the New Gravitational Force
Using the new parameters, let's calculate the gravitational force between the two objects:
F' = G * (2m * 2m) / (2r)^2
= G * 4 * (m * m) / (4 * r^2)
= G * (m * m) / r^2
= F
Comparing the Forces
As we can see, the new gravitational force F' is equal to the original gravitational force F. Therefore, the correct answer is option 'A': F.
Explanation
The gravitational force between two objects depends on their masses and the distance between them. In this problem, when the masses of the objects are doubled and the distance between them is also doubled, the new gravitational force remains the same as the original force. This is because the effect of doubling the masses and doubling the distance cancels out each other, resulting in the same gravitational force as before.
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 two objects
- r is the distance between the centers of the two objects
Given Parameters
In this problem, we are given the following parameters:
- Two objects with mass m each
- Separated by a distance r
Calculating the Gravitational Force
Let's calculate the gravitational force between the two objects using the given parameters:
F = G * (m * m) / r^2
Increasing the Mass and Distance
Now, let's consider the scenario where the masses of the two objects are doubled and the distance between them is also doubled:
- Mass of each object = 2m
- Distance between the objects = 2r
Calculating the New Gravitational Force
Using the new parameters, let's calculate the gravitational force between the two objects:
F' = G * (2m * 2m) / (2r)^2
= G * 4 * (m * m) / (4 * r^2)
= G * (m * m) / r^2
= F
Comparing the Forces
As we can see, the new gravitational force F' is equal to the original gravitational force F. Therefore, the correct answer is option 'A': F.
Explanation
The gravitational force between two objects depends on their masses and the distance between them. In this problem, when the masses of the objects are doubled and the distance between them is also doubled, the new gravitational force remains the same as the original force. This is because the effect of doubling the masses and doubling the distance cancels out each other, resulting in the same gravitational force as before.
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Community Answer
The gravitational force between two objects each of mass m, separated ...
Gravitational force between two objects is mathematically represented as:
F = G * (m1*m2) / r2
Applying the Law of Gravitation to the Given Problem
Given that the initial force F is due to two objects each of mass m separated by a distance r.
Substituting these into the formula gives:
F = G * (m*m) / r2
The problem then states that the mass of each of the objects is doubled (to 2m) and the distance between them is also doubled (to 2r).
The new force F' using these values in the formula would be: F' = G * (2m*2m) / (2r)2
Simplifying this gives:
F' = 4G * (m*m) / 4*r2
This simplifies further to:
F' = G * (m*m) / r2
Comparing this with the original equation for F, we find that:
F' = F
Thus, the force remains the same (F) even when the mass of each of the objects is doubled and the distance between them is also doubled. Hence, the correct answer is A: F.
F = G * (m1*m2) / r2
Applying the Law of Gravitation to the Given Problem
Given that the initial force F is due to two objects each of mass m separated by a distance r.
Substituting these into the formula gives:
F = G * (m*m) / r2
The problem then states that the mass of each of the objects is doubled (to 2m) and the distance between them is also doubled (to 2r).
The new force F' using these values in the formula would be: F' = G * (2m*2m) / (2r)2
Simplifying this gives:
F' = 4G * (m*m) / 4*r2
This simplifies further to:
F' = G * (m*m) / r2
Comparing this with the original equation for F, we find that:
F' = F
Thus, the force remains the same (F) even when the mass of each of the objects is doubled and the distance between them is also doubled. Hence, the correct answer is A: F.
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