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?
A). It becomes four times stronger
B). It becomes half as strong
C). It remains the same
D). 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.
Therefore, the correct answer is:
D) It becomes twice as strong
The gravitational force between two objects is directly proportional to the mass of both objects and inversely proportional to the square of the distance between them.
In this case, if the mass of one object is doubled while the distance remains the same, we can determine the change in gravitational force.
If we denote the original mass as M and the original gravitational force as F, and the new mass as 2M, we can write the equation for the original gravitational force as:
F = G x M x M / d^2
where G is the gravitational constant and d is the original distance between the objects.
Now, let's calculate the new gravitational force (F') using the new mass (2M):
F' = G x (2M) x M / d^2
The new gravitational force can be simplified as:
F' = 2 x F
This means that the new gravitational force is twice the original force. Therefore, the correct answer is:
D). 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.
According to Newton's law of universal gravitation, 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 expressed as:
F = (G * m₁ * m₂) / r²
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 their centers
In this case, we are keeping the distance constant while doubling the mass of one object. Let's say the original mass of the object is M, so after doubling, the new mass would be 2M.
Now, let's compare the gravitational forces before and after doubling the mass.
Original Force (F₁) = (G * M * M) / r²
New Force (F₂) = (G * (2M) * M) / r²
Simplifying the equations, we find that the ratio of the new force to the original force is:
F₂ / F₁ = [(G * (2M) * M) / r²] / [(G * M * M) / r²]
Canceling out G and r² terms, we get:
F₂ / F₁ = (2M * M) / (M * M)
F₂ / F₁ = 2
So the new force (F₂) is twice the original force (F₁). Therefore, the gravitational force becomes twice as strong when the mass of one object is doubled while the distance remains the same.
Therefore, the correct answer is D) It becomes twice as strong.