Question

Seven 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/10. Find the x-coordinate fo the centre of mass relative to the origin shown.

Answer 1

Let OX be the X-axis and point O (0, 0) be the origin of the system.
The mass of each brick is M.
The length of each brick is L.
Each brick is displaced with respect to another in contact by a distance  \[\frac{L}{10}\] .

∴ The X-coordinate of the centre of mass is given as,
\[X_{cm} = \frac{1}{7 m\frac{L}{10}}^\left\{ \frac{mL}{2} + m\left( \frac{L}{2} + \frac{L}{10} \right) + . . . . . . . . . . + m\left( \frac{L}{2} \right) \right\} \]
\[ X_{cm} = \frac{\frac{L}{2} + \frac{L}{2} + \frac{L}{10} + \frac{L}{5} + \frac{L}{2} + \frac{3L}{10} + \frac{L}{2} + \frac{L}{5} + \frac{L}{2} + \frac{L}{10} + \frac{L}{2}}{7}\]
\[ = \frac{7\frac{L}{2} + 5\frac{L}{10} + 2\frac{L}{5}}{7} = \frac{22L}{35}\]
The X-coordinate of the centre of mass relative to the origin is \[\frac{22L}{35}\]