Respuesta :
Answer
given,
copper rod length = 50 cm
density of the copper = 8.92 g/cm³
iron rod length = 50 cm
density of iron = 7.86 g/cm³
mass of iron = density × volume
        m_i = 7.86 × A × l/2
        m_c = 8.96 × A × l/2
taking  the intersection of copper and iron rod be starting point cooper side is taken as positive side and iron side length is taken to be  -ve side.
center of mass
 = [tex]\dfrac{m_i\times \dfrac{-l}{4}+m_c\times \dfrac{l}{4}}{m_i+m_c}[/tex]
 = [tex]\dfrac{7.86\times A \times \dfrac{l}{2}\times \dfrac{-l}{4}+8.96\times A \times \dfrac{l}{2}\times \dfrac{l}{4}}{7.86\times A \times \dfrac{l}{2}+8.96\times A \times \dfrac{l}{2}}[/tex]
 = [tex]\dfrac{7.86\times \dfrac{-l}{4}+8.92\times \dfrac{l}{4}}{7.86+8.92}[/tex]
 = [tex]\dfrac{1.06\dfrac{l}{4}}{16.78}[/tex]
 = 0.015793 m
 = 1.579 m (+ve)
center of mass shift to cooper because cooper is heavy.
The center of mass is at -1.58 cm, that is towards the left of the origin, or towards the copper end.
Given information:
Let the length of the rod is 2l = 100cm = 1m, then
copper rod length l = 50 cm
density of the copper = 8.92 g/cm³
iron rod length l = 50 cm
density of iron = 7.86 g/cm³
Let the cross-sectional area of the rod be A, so
mass of iron = density × volume
[tex]m_i = 7.86 \times A \times l[/tex]
mass of copper
[tex]m_c = 8.92 \times A \times l[/tex]
Center of mass :
According to the question, the origin lies at the midpoint of the rod, that is the position of the joint between iron and copper.
let us assume that the copper rod is at the left of the origin and the iron rod is at the right of the origin, and both the rods are uniform, so the center of mass of the individual rods be at their midpoint, that is [tex]\frac{l}{2}[/tex], so the center of mass of the combined rod is :
[tex]cm = \frac{m_c\times(-l/2)+m_i\times(l/2)}{m_c+m_i}\\\\cm= \frac{ 8.92 \times A \times l\times(-l/2)+7.86 \times A \times l\times(l/2)}{8.92 \times A \times l+7.86 \times A \times l} \\\\cm=\frac{-0.53\times l}{16.78}=\frac{-0.53\times50}{16.78}\\\\cm= -1.58\;cm[/tex]
The negative sign indicates that the center of mass is towards the left.
Learn more about the center of mass:
https://brainly.com/question/3391593?referrer=searchResults
