Answer
11 cm
Work Step by Step
Center of mass of right vertical rod is $\left( {L, - \frac{L}{2}} \right)$
Center of mass of left vertical rod is$\left( {0, - \frac{L}{2}} \right)$
Center of mass of horizontal rod is $\left( {\frac{L}{2},0} \right)$
We know that the formula for finding the x-coordinate of the center of mass is:
${x_{c.o.m.}} = \frac{{{m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3}}}{{{m_1} + {m_2} + {m_3}}}$
We know that ${m_1} = 14g$,${m_2} = 42$ and ${m_3} = 14\,g$
We also know that ${x_1} = 0$, ${x_2} = \frac{L}{2}$ and ${x_3} = L$.
Substituting these values in the formula and simplifying, we get
${x_{c.o.m.}} = \frac{L}{2} = 11\,cm$
