Three small spheres, having masses m1 = 1 kg, m2 = 3 kg, and m3 = 4 kg, are held fixed on the x axis in deep space where the effects of earth's gravity can be neglected. they are positioned at x = 0, x = 3 m, and x = 6 m, respectively. what is the magnitude of net gravitational force on m2?

towards the mass

Explanation: We know that the gravitational force is a long range force which is always attractive in nature.

Given that:

The masses are positioned on X-axis at the following points:

Mathematically:

Gravitational force on mass due to mass is given by

...................(1)

Similarly, gravitational force on mass due to mass is given by

............................(2)

Now, put the respective values in the above equations.

Again,

∵Mass is in the middle of the masses & therefore the forces   & will attract them in radially opposite direction.

∴ towards the mass

The magnitude of the net force on is

Solution:

As per the question:

Respective positions of the above mentioned masses are:

x = 0 m

x = 3 m

x = 6 m

Now,

We know that the gravitational force between two masses separated by some distance is given by:

Therefore. the net gravitational force on is given by:

where

G = Gravitational constant

it is the second option.