Torque Balance

In the \(xy\) coordinate system, two massive point-particles are attached to a pivot point by mass-less rigid rods. There is one particle of mass \(1kg\), situated \(1m\) to the left of the pivot. There is another particle of mass \(M\) situated \(2m\) to the right of the pivot.

A third point-particle of mass \(1kg\) is located \(1m\) to the left and \(1m\) down from the other \(1kg\) particle. This particle is fixed in place.

The pivot point is fixed in place, and the attached particles are free to rotate around it.

If the system is in static equilibrium, determine the value of \(M\) (in \(kg\)), to 2 decimal places.

Note: There is no ambient gravitational field in this problem


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