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

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

1. $\frac{\mathrm{L}}{4}$
2. $\frac{\mathrm{L}}{2}$
3. $\left(\frac{3}{2}\right) \mathrm{L}$
4. $\left(\frac{11}{12}\right) \mathrm{L}$

Solution

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

Asked in: TEST SERIES MHT-CET Full Test 6

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