Answer to Question #247105 in Physics for Molina

Question

Determine the x-coordinate of the center of gravity of a system of weights composed of a uniform density
meterstick of mass 0.40 kg, a 0.60 kg object hung from the 20-cm mark and 0.50 kg mass hung from the 70-cm
mark of the meterstick.

Answer 1

Assume the center of mass is x cm from 0 mark to the fulcrum:

$$x=\frac{0.6·20+0.5·70+0.4x^2/(2)+0.4(1-x)·(x+(1-x)/2)}{0.6+0.5+0.4}=\\\space\\=31.47\text{ cm}.$$