Three bricks each of length L and mass M are arranged as shown from...

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 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

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

Options

A $L / 4$
B $L / 2$
C $(3 / 2) L$
D $(11 / 12) L$

Correct answer

D. $(11 / 12) L$

Step-by-step 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}

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