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 $\frac{L}{10}$. Find the x-coordinate of the centre of mass relative to the origin shown.

• A. $\frac{21}{35}L$
• B. $\frac{L}{2}$
• C. $\frac{22L}{35}$
• D. None of these

Answer 1

The correct option is C $\frac{22L}{35}$

Com of each brick is at $\frac{L}{2}$
Hence, according to their positions.

Now, using the expression of com for multiple particles.
By symmetry,y-coordinate of com will not displace.
$X_{com}=\frac{m_1{x}_1+m_2{x}_2+\dots \dots m_7{x}_7}{m_1+m_2+\dots \dots m_7}$
$=\frac{2m.\frac{L}{2}+2m.\frac{6L}{10}+2m.\frac{7L}{10}+\frac{8L}{10}}{7m}$
$=\frac{44L}{70}=\frac{22L}{35}$