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 $\frac{\mathrm{L}}{4}$
B $\frac{\mathrm{L}}{2}$
C $\left(\frac{3}{2}\right) \mathrm{L}$
D $\left(\frac{11}{12}\right) \mathrm{L}$

Correct answer

D. $\left(\frac{11}{12}\right) \mathrm{L}$

Step-by-step solution

x_{1}=\frac{\mathrm{L}}{2}, x_{2}=\mathrm{L}, x_{3}=\frac{5 \mathrm{ L}}{4}\therefore x_{\mathrm{CM}}=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}}{m_{1}+m_{2}+m_{3}}=\frac{\mathrm{M} \times \frac{\mathrm{L}}{2}+\mathrm{M} \times \mathrm{L}+\mathrm{M} \times \frac{5 \mathrm{ L}}{4}}{\mathrm{M}+\mathrm{M}+\mathrm{M}}=\frac{11 \mathrm{ L}}{12}

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