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 of the centre of mass relative to the origin $O$ shown.

• A. $\frac{L}{2}$
• B. $22L/35$
• C. $\frac{11L}{35}$
• D. $\frac{L}{4}$

Answer 1

The correct option is C $\frac{11L}{35}$

Each brick has a mass $M$ and length $L$ and each brick is displaced by $L/10$

According to teh question

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

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

$\Rightarrow x_{xm}=\frac{11}{35}L$