help me set this up

Question

A meter stick has a 300 g mass at the 0 cm mark and a 30 g at the 100 cm mark. If the meter stick has a mass of 120 g, how far from the 0 cm mark should a fulcrum be placed to balance the meter stick? Express the answer in centimeters.

Answer 1

Let x = distance from fulcrum to 300 gram mass and 1-x = distance from fulcrum to 30 gram mass (meters)

Set this up as a moment problem and the governing equation is:

You can convert to weights with .3 kg(9.8 m/s2) = weight at the 0 mark

and .03 kg(9.8 m/s2) = weight at the 100 cm mark

Then

2.94x = .294(1-x) or x = .090909...meters = 9.0909... cm