Question

Seven homo genous bricks , each of length $L$ , are arranged as shown below. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Find $X$ coordinate of the centre of mass relative to the origin shown

• A. $\frac{11L}{60}$
• B. $\frac{7}{10}L$
• C. $\frac{4L}{35}$
• D. None of these

Answer 1

The correct option is D

None of these

Let '$O$' (0, 0) be the origin of the system.
Each brick is 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\
$\overline{X_{c}m}=\frac{m\left(\frac{L}{2}\right)+m(\frac{L}{2}+\frac{L}{10})+m(\frac{L}{2}+\frac{3L}{10})+m(\frac{L}{2}+\frac{3L}{10}-\frac{L}{10})+m(\frac{L}{2}+\frac{L}{10})+m\left(\frac{L}{2}\right)}{7m}$
$=\frac{\frac{L}{2}+\frac{L}{2}+\frac{L}{10}+\frac{L}{2}+\frac{L}{5}+\frac{L}{2}+\frac{3L}{10}+\frac{L}{2}+\frac{L}{5}+\frac{L}{2}+\frac{L}{10}+\frac{L}{2}}{7}$
$=\frac{\frac{7L}{2}+\frac{5L}{10}+\frac{2L}{5}}{7}=\frac{35L+5L+4L}{10\times 7}=\frac{44L}{70}=\frac{11}{35}L$