the center of gravity of a 100-g stick is located at 50 cm mark and the stick is supported at 60cm. mark, Where must an 80g object be hung in order to have equilibrium?

Answer 1

Let the fulcrum be at 60 from the left end.

60g have center of mass 30 to the left
40g have center of mass 20 cm to the right

The 80g mass must be on the right side, at a distance x such that

60*30 = 40*20 + 80x

so, its location is at 60+x cm from the left.