Question

An infinite number of bricks are placed one over the other as shown in the figure. Each succeeding brick havinghalf the length and breadth of its preceding brick and the mass of each succeeding bricks being1/4th of the preceding one, take 'O' as the origin, the x-coordinate of centre of mass of the system of bricks is:-:​

Answer 1

the x-coordinate of centre of mass of the system of bricks is 2a/7

Explanation:

As we know that we have

$y_{cm} = \frac{m_1y_1 + m_2y_2 + m_3y_3 + m_4y_4......................}{m_1 + m_2 + m_3...}$

now we know that center of mass of each brick must be at mid position of the brick

so we will have

$x_{cm} = \frac{m\frac{a}{2} + \frac{m}{4}\frac{a}{4} + \frac{m}{16}\frac{a}{8}..............}{m + m/2 + m/4...................}$

$x_{cm} = \frac{\frac{ma/2}{1 - 1/8}}{\frac{m}{1 - 1/2}}$

$x_{cm} = \frac{\frac{4ma}{7}}{2m}$

$x_{cm} = \frac{2a}{7}$

here a = size of first brick along x direction

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Topic : Center of mass

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