Answer
The fulcrum should be placed 29.8 cm from the left end.
Work Step by Step
We can find the center of gravity $x_{cog}$ of these three masses. To find the center of gravity, we will consider the distance of each mass from the left end of the bar. Note that the center of mass of the bar is located at the midpoint.
$x_{cog} = \frac{m_1~r_1+m_2~r_2+m_3~r_3}{m_1+m_2+m_3}$
$x_{cog} = \frac{(0.055~kg~g)(0)+(0.120~kg)(25.0~cm)+(0.110~kg)(50.0~cm)}{0.055~kg+0.120~kg+0.110~kg}$
$x_{cog} = 29.8~cm$
The fulcrum should be placed 29.8 cm from the left end.
