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.
Figure

Answer 1

The X-coordinate of the center of mass relative to the origin of seven homogeneous bricks, each of length L and each brick is displaced with respect to the one in contact by $\frac{L}{10}$ is $\frac{22 L}{35}$  

Explanation:

Seven homogeneous bricks are arranged as shown in the figure, each of which is length L. With respect to the one in contact with  $\frac{L}{10}$ per brick is displaced  

For a better understanding see figure.

Take ' O ' (0, 0) to be system origin.

Given:-

Every brick is ' M ' in mass and ' L ' in mass.

By "$\frac{L}{10}$" each brick is displaced in relation to one in touch

X Mass Center Coordination:

$X_(center of mass)$  

= $\frac{m \frac{L}{2}+m\left(\frac{L}{2}+\frac{L}{10}\right)+m\left(\frac{L}{2}+\frac{2 L}{10}\right)+m\left(\frac{L}{2}+\frac{3 L}{10}\right)+m\left(\frac{L}{2}+\frac{3 L}{10}-\frac{L}{10}\right)+m\left(\frac{L}{2}+\frac{L}{10}\right)+m \frac{L}{2}}{7 m}$

$X_(center of mass)$ = $\frac{m\left[\frac{L}{2}+\left(\frac{L}{2}+\frac{L}{10}\right)+\left(\frac{L}{2}+\frac{2 L}{10}\right)+\left(\frac{L}{2}+\frac{3 L}{10}\right)+\left(\frac{L}{2}+\frac{3 L}{10}-\frac{L}{10}\right)+\left(\frac{L}{2}+\frac{L}{10}\right)+\frac{L}{2}\right]}{7 m}$

$X_(center of mass)$ = $\frac{\left[\frac{L}{2}+\left(\frac{L}{2}+\frac{L}{10}\right)+\left(\frac{L}{2}+\frac{2 L}{10}\right)+\left(\frac{L}{2}+\frac{3 L}{10}\right)+\left(\frac{L}{2}+\frac{3 L}{10}-\frac{L}{10}\right)+\left(\frac{L}{2}+\frac{L}{10}\right)+\frac{L}{2}\right]}{7}$

$X_(center of mass)$ = $\frac{\left[\frac{7 L}{2}+\frac{5 L}{10}+\frac{2 L}{5}\right]}{7}$

$X_(center of mass)$ =   $\frac{\left[\frac{35 L+5 L+4 L}{10}\right]}{7}$

$X_(center of mass)$ =  $\frac{35 L+5 L+4 L}{7 \times 10}$

$X_(center of mass)$ = $\frac{44 L}{70}$

$X_(center of mass)$ = $\frac{22 L}{35}$

The x- coordinate of the center of mass relative to the origin is $\frac{22 L}{35}$.

Answer 2

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$\frac{22l}{35}$

hope it help