Two point masses at a given distance exert a gravitational interaction force on each other having a magnitude F. If one mass is doubled the other mass is halved and the distance between them is tripled, the resulting interaction force magnitude.
(a) F (b) 4F (c) 4F/9 (d)F/9
Answers
Answer:
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Explanation:
Correct Answer is (D) F/9
The magnitude of the resulting interaction force between the two objects is equal to F/9. (Option-D)
Given,
The magnitude of the gravitational interaction force acting between two point masses at a given distance = F
To find,
The magnitude of the resulting interaction force between the two objects if one mass is doubled the other mass is halved and the distance between them is tripled.
Solution,
We can simply solve this numerical problem by using the following process:
As per the gravitational law;
The gravitational force acting between two bodies of mass M and m, separated by a distance d, is mathematically represented as;
F = (G ×M×m)/d^2,
where G = Gravitational constant
= 6.67408 × 10-11 m3 kg-1 s-2
{Statement-1}
Let us assume that the initial mass of both objects is M and m units, with their initial distance of separation, is "d" units, respectively.
Now, according to the question;
The magnitude of the gravitational interaction force acting between two point masses at a given distance = F
=> (G ×M×m)/d^2 = F
{Equation-1}
Now, according to the question;
The final masses are 2M and m/2 units.
The distance between the two masses is now 3d units.
So now, the magnitude of the resulting interaction force between the two objects
= (G × 2M × m/2 )/(3d)^2
= (G ×M×m)/9d^2
= 1/9 × (G ×M×m)/d^2
= 1/9 × F
{according to equation-1}
= F/9
Hence, the magnitude of the resulting interaction force between the two objects is equal to F/9. (Option-D)