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Question

Seven homogeneous bricks, each of length $$L$$, are arranged as shown in figure. Each brick is displaced with respect to the one in contact by $$L/10$$. Find the $$x-$$coordinate of the centre of mass relative to the origin $$O$$ shown. 

1252749_e5f886aa099c4185b1828b0c52d81e1c.PNG


A
L2
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B
22L/35
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C
11L35
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D
L4
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Solution

The correct option is C $$\dfrac{11L}{35}$$
Each brick has a mass $$M$$ and length $$L$$ and each brick is displaced by $$L/10$$
According to teh question
$${X}_{cm}=\cfrac{m(L/2)+m(L/2+L/10)+m(L/2+2L/10)+m)L/2+3L/10-L/10)+m(L/2+3L/10)+m(L/2+L/10)+m)L/2)}{7m}$$
$${x}_{cm}=\cfrac{\cfrac{7L}{2}+\cfrac{5L}{10}+\cfrac{2L}{5}}{7}$$
$$\Rightarrow  {x}_{xm}=\cfrac{11}{35}L$$

Physics

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