Hi there!
Assuming the ruler has a uniform mass-density throughout, the center of mass of the ruler is at the half-way point, or 50 cm.
We can use a summation of torques about the fulcrum:
[tex]\large\boxed{\Sigma \tau = rF}[/tex]
r = distance from fulcrum to force (m)
F = force (N)
On one side of the fulcrum, there is a counterclockwise torque created by the hanging mass and the mass of the ruler.
For the system to be balanced, the torques sum to zero. Thus:
[tex]\large\boxed{\tau_{cc} = \tau_{ccw}}[/tex]
For proper physics, we can convert cm to m and g to kg.
Torque exerted by the hanging mass:
τ = Mg(.35 - .10) = Mg(.25)
Torque exerted by the ruler:
τ = (.1)(g)(.50 - .35) = 0.015g
Set the two equal:
0.015g = Mg(.2)
Cancel out 'g':
0.015 = .25M
M = 0.06 kg ⇒ 60 grams
