question_answer

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)  \[(3/2)L\]           

D)        \[(11/12)L\]

E)  \[(5/6)L\]

Correct Answer: D

Solution :

\[{{x}_{1}}=\frac{L}{2}\] \[{{x}_{2}}=L\] \[{{x}_{3}}=L+\frac{L}{4}\] \[{{x}_{3}}=\frac{5L}{4}\] \[\therefore \]  \[{{x}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{2}}{{x}_{3}}}{3m}\]                 \[=\frac{\frac{mL}{2}+mL+\frac{m5L}{4}}{3m}\]                 \[=\frac{11L}{12}\]