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It's basically just balancing moments; Since the entire set up can be assumed to be stationary once the 50g mass is added, the tension in the rope is
Tension = (20/1000) * 9.81 = 0.1962 N
This means that the moment caused by the suspended mass is
Moment = Tension * Distance from pivot = 0.1962 * 0.6 = 0.11772 Nm^-1
This is an Anti-Clockwise moment because the force will pull the left side upwards (and thus in the ACW direction) if it is allowed to act alone.
The weight of the ruler can be assumed to act from its center (at the 50 cm mark), and is a Clockwise moment, because the force will pull the right side of the ruler down (and thus CW) if it is allowed to act alone.
The value of this moment is :
0.1 * 9.81 * 0.1 = 0.0981 Nm^-1
So if the system has to be in equilibrium, then the net moment has to be zero. But the ACW moment due to the 20g mass is more than the CW moment due to the mass of the ruler, so we need to position the 50g mass in such a place that it will exert a CW moment to make the CW moment equal to the ACW moment. This means that the 50g mass will have to be positioned to the right of the pivot, and it will have to exert a moment of magnitude
0.11772 - 0.981 = 0.01962 Nm^-1 (this is the difference in moments in the current situation).
Therefore,
(50/1000) * 9.81 * D = 0.01962
D = 0.04 m = 4 cm to the right of the pivot.
Since the pivot is at 40 cm, the mass will be placed at the 44 cm mark.
Hope this helped!
Good Luck for all your exams!