Four identical masses are placed at the four corners of a square and we need to find the effective gravitational force at any one corner and the problem is as shown in the diagram below.

Four identical masses are placed at the four corners of a square and we need to find the effective gravitational force at any one corner and the problem is as shown in the diagram below.

Solution

On any one particle, there is gravitational force of attraction due to the other two. We can find each force using the newton's law of gravitation. The diagram is as shown below.