Question

Two massive objects are fixed in position. A third object is placed directly between the first two at the position at which the total gravitational force on the third object due to the two massive objects is zero. The object is displaced slightly toward one of the two massive objects, the total gravitational force on the third object is now

Answer 1

Answer:

Explanation:

Be M1 and M2 the two massive objects and m the third one

The gravitational force over the third object at the beginning is zero (assuming that the position of the third object is x=0)

$F_{m}=-G\frac{mM_{1}}{x_{1}^{2}}-G\frac{mM_{2}}{x_{2}^{2}}=0$

when the third object is displaced we have that the new position is x=Δx. Hence

$F_{m}=-G\frac{mM_{1}}{(-x_{1}+\Delta x)^{2}}-G\frac{mM_{2}}{(x_{2}-\Delta x)^{2}}$

I attached a scheme of the system

I hope this is useful for you

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