Question

The end of two thin steel rods of equal length are welded together to make a right angled frame. Locate the frame's center of mass?

Answer 1

Let `land m` be length and mass respectively of each thin rod.
Let us choose origin of coordinate system at the right angle of the frame, with one rod aligned along the `x`-axis and other rod along the `y`-axis.

Center of mass of rod lying on `x`-axis is at its mid-point

`(x_1,y_1)=(l/2,0)`

Center of mass of rod lying on `y`-axis is at its mid-point

`(x_2,y_2)=(0,l/2)`
Now `x_"com" =[ m_1x_1 + m_2x_2]/[m_1+m_2] =[ (m)(l/2) + 0]/[m + m] = l/4`
Similarly `y_"com" = [m_1y_1 + m_2y_2]/[m_1+m_2] = [0+(m)l/2 ]/[m+m] = l/4`
`:.vecr_"com" = l/4hati + l/4hatj`