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

Question

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\

Professor PC Thomas Classes · Answer

\From figure,\ $\mathrm{x}_{1}=\frac{\mathrm{L}}{2}, \mathrm{x}_{2}=\frac{\mathrm{L}}{2}+\frac{\mathrm{L}}{2}=\mathrm{L}$\ And $x_{3}=\frac{L}{2}+\frac{L}{4}+\frac{L}{2}=\frac{5 L}{4}$\ $	herefore \mathrm{X}_{\mathrm{CM}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{2} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}$\ $=\frac{M 	imes \frac{L}{2}+M 	imes L+M 	imes \frac{5 L}{4}}{M+M+M}=\frac{\frac{11}{4} M L}{3 M}=\frac{11 L}{12}$\