Two identical objects are kept at a distance R .what will be the change in gravitational force if one more identical object (same mass) is placed in the mid of the two objects?
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Answers
Answer:
F = (G m1m2)/r2
Where m1m2 = the masses of the two bodies,
r = distance between them
G = gravitational Constant
When the distance is reduced to half i.e. r’ = (1/2) r then,
F’ = (G m1m2)/r2
= (G m1m2)/(r/2)2
= (4 G m1m2)/ (r2) = 4F
Therefore when the distance between the objects is reduced to half, then the force of gravitation increases by four times the original force.
The gravitation between the two objects will remain same. However, the net force on both the objects will change due to exertion of gravitational force by the object placed in between.
Earlier, net force on each of the objects was GM^2 / R^2
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Now, when one more object is placed in between, it exerts force on both the objects, which is equal to 4GM^2 /R^2
So, Net Force on each of the two objects becomes 5 GM^2 /R^2