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Q.

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 $\frac{x}{12} L .$ The value of x is

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answer is 11.

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Detailed Solution

From figure,

Question Image

$x_{1} = \frac{L}{2}, x_{2} = \frac{L}{2} + \frac{L}{2} = L$

$x_{3} = \frac{L}{2} + \frac{L}{4} + \frac{L}{2} = \frac{5 L}{4}$

$∴ x_{C M} = \frac{M_{1} x_{1} + M_{2} x_{2} + M_{3} x_{3}}{M_{1} + M_{2} + M_{3}}$

$= \frac{M \times \frac{L}{2} + M \times L + M \times \frac{5 L}{4}}{M + M + M}$

$= \frac{\frac{11}{4} M L}{3 M} = \frac{11 L}{12}$

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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 x12L. The value of x is