To solve the exercise, the key concept to be addressed is the Mass Center.
The center of mass of an object is measured as,
[tex]X_{cm} = \frac{\sum m_ix_i}{\sum m_i}[/tex]
[tex]X_{cm} = \frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}[/tex]
Our values are given by,
[tex]x_1 = 50cm[/tex]
[tex]m_1 = ?[/tex]
[tex]x_2 =28.8cm[/tex]
[tex]m_2 = 4.79g[/tex]
[tex]x_3 = 28.8cm[/tex]
[tex]m_3 = 4.79g[/tex]
[tex]X_{cm} = 38.4cm[/tex]
Replacing the values in our previous equation we have,
[tex]X_{cm} = \frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}[/tex]
[tex]38.4 = \frac{m_1(50)+2(28.8*4.79)}{m_1+2*4.79}[/tex]
[tex]38.4(m_1+2*4.79)= m_1(50)+2(28.8*4.79)[/tex]
[tex]38.4m_1 +367.872 = 50m_1+275.904[/tex]
[tex]11.6m_1 = 91.968[/tex]
[tex]m_1 = 7.928g[/tex]
Therefore the mass of the meter stick is 7.928g
