Question

Five homogeneous bricks, each of length $L$, are arranged as shown in figure. Each brick is displaced with respect to the one in contact by $L/5$. Find the x-coordinate of the centre of mass relative to the origin $O$ shown.

Answer 1

$\overrightarrow{X_{cm}}=\frac{m(\frac{L}{2}+\frac{L}{2}+\frac{L}{5}+\frac{L}{2}+\frac{2L}{5}+\frac{L}{2}+\frac{L}{5}+\frac{L}{2})}{5m}$

where,

$\frac{L}{2}$ - Ist block

$\frac{L}{2}+\frac{L}{5}$ - 2nd block

$\frac{L}{2}+\frac{2L}{5}$ - 3rd block

$\frac{L}{2}+\frac{L}{5}$ - 4th block

$\frac{L}{2}$ - 5th block

COM $=\frac{33L}{50}$