Three identical uniform bricks of mass m and length l are stacked on top of each other. (a) what is the maximum distance d so that the stack does not tumble over? (hint: consider the top two bricks first, then add the bottom brick) (b) what is the maximum distance d that can be achieved by optimal stacking of an infinite number of bricks?

Explanation:

Given

Three blocks are placed over each other at a certain distance.

Center of gravity of each block is at distance of 0.5 L from one end of block.

First We consider block 1 and 2

Block 1 center of gravity will try to tumble the block 1 if center of gravity torque goes beyond 0.5 L of second block.

i.e. maximum distance up to which block 1 is placed over block 2 is

combined center of gravity of 1 and 2 is

Center of gravity

Now consider block 2 and 3

Combined center of gravity of  block 1 and 2 will tumble over when their Center of gravity goes beyond edge of block 1

i.e. maximum value of

(b) As the no of blocks increases center of gravity increases so maximum value of

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