Question

Seven homogeneous bricks,each of length L, are arranged as shown in figure (9-E2).Each brick is displaced with respect to the one in contact by L/10.Find the x-coordinate of the centre of mass relative to the origin shown.

Answer 1

Let '0' (0,0) be the origin of the system.Each brick is of mass 'M' and length 'L',Each brick is displaced w.r.t. one in contact by,\frac{L}{10}.

$\therefore$ The X coordinate of the centre of mass $X_{cm}$

$=\frac{1\{\frac{mL}{2}+m(\frac{L}{2}+\frac{L}{10})+........+m\left(\frac{L}{2}\right)\}}{7m\frac{L}{10}}$

$X_{cm}=\frac{\frac{L}{2}+\frac{L}{2}+\frac{L}{10}+\frac{L}{5}+\frac{L}{2}+\frac{3L}{10}+\frac{L}{2}+\frac{L}{5}+\frac{L}{2}+\frac{L}{10}+\frac{L}{2}}{7}$

$=\frac{7\frac{L}{2}+5\frac{L}{10}+2\frac{L}{5}}{7}=\frac{22L}{35}$