Three bricks each of length $L$ and mass $M$ are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is

• A

  $L / 4$
• B

  $L / 2$
• C

  $(3 / 2) L$
• Correct answer
  D

  $(11 / 12) L$

Solution

From figure,
$\begin{aligned} & x_1=\frac{L}{2}, x_2=\frac{L}{2}+\frac{L}{2}=L \\ & \text { and } x_3=\frac{L}{2}+\frac{L}{4}+\frac{L}{2}=\frac{5}{4} L \\ & \therefore X_{C M}=\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3} \\ & =\frac{M \times \frac{L}{2}+M \times L+M \times \frac{5 L}{4}}{M+M+M}=\frac{\frac{11}{4} M L}{3 M}=\frac{11}{12} L\end{aligned}$

Hence, the correct answer is option: 'D'.