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As we learnt in
Point of application of force -
Point at which if net force is assumed to be acting then it will produce the same effect of both translation & rotation.
-
For balance
Anticlockwise Moment = Clockwise Moment
i.e. Load
load arm = effect 
effort arm
When 5 mg weight is placed, load arm shifts to left side, hence left arm becomes shorter than right arm.
Option 1)
Left arm is longer than the right arm
This is an incorrect option.
Option 2)
Both the arms are of same length
This is an incorrect option.
Option 3)
Left arm is shorter than the right arm
This is the correct option.
Option 4)
Every object that is weighed using this balance appears lighter than its actual weight.
This is an incorrect option.