We know that when two equal masses are placed on a line then, gravitational force on a third mass is zero due to these two masses when the third is placed at the centre of line joining the two masses. But if third mass is placed anywhere else on the x-axis, the gravitational force acts on that mass due to these two masses. Consider a system shown in figure.

In this system two point masses of mass M each are placed at y-axis at a distance a from origin and these masses are fixed. If a third point mass of mass m is released at a distance x from origin on x-axis, then answer the following questions.
The net force on the mass m is
when `vec(x)` is position vector of the point mass of mass m.

Options

A. `vec(F)=-(2GMm vec(x))/((a^(2)+x^(2))^(3//2))`
B. `vec(F)=(2GMm vec(x))/((a^(2)+x^(2))^(3//2))`
C. `vec(F)=(-GMm vec(x))/((a^(2)+x^(2))^(3//2))`
D. `vec(F)=(GMm vec(x))/((a^(2)+x^(2))^(3//2))`

Answer

A