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An infinite number of bricks are placed ...

An infinite number of bricks are placed one over the other as shown in the figure . Each succeeding brick having half the length and breadth of its preceding brick and the mass of each succeeding bricks being `(1)/(4)` th of the preceding one . Take 'O' as the origin . The x -coordinate of centre of mass of the system of bricks is :

A

`-a//7`

B

`3a//7`

C

`-3a//7`

D

`-2a//7`

Text Solution

Verified by Experts

`X_(com)=([Mxx(a)/(2)+(M)/(2)xx(a)/(4)+(M)/(16)xx(a)/(8)+.....oo])/(M+(M)/(4)+(M)/(16)+......oo)=-(3a)/(7)`
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