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I came across an article that 6 year olds in the UK will be asked questions like this in maths class:

Fulcrum question

The question is intended to be an algebra problem of balancing the total weight on each side (ignore the physics and distances).

In that case, 2 circles weigh 18 kg, so a single circle weighs 9 kg. Then we can solve the square has to be 27 kg, so two squares are 54 kg. This is the correct answer.

But this seems really wrong from a physics perspective! The diagrams clearly show objects at different distances. Eventually the kids will have to learn to balance the forces, where force = (mass)(distance).

All of the problems I ever solved object 1 (distance $d_1$ and mass $m_1$) on the left and object 2 (distance $d_2$ and mass $m_2$) on the right, so it was then about solving:

$$ d_1 m_1 = d_2 m_2 $$

How would you solve the problem above with proper physics? Basically what's the technique for balancing seesaws with multiple weights, where some weights are stacked on top of each other?

I honestly don't know how this kind of problem could make it into a math classroom--did no one study physics? It would have been better if they just said to make the total weight on left and right sides equal instead of "balancing" the sides. The diagram as drawn is very bizarre.

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    $\begingroup$ I used to hate this kind of question precisely because of the problem you bring up: I would somehow frustratingly try to divine a radius for the balls and work out distances. $\endgroup$ Aug 23, 2017 at 2:16

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You would set the "clockwise" torque equal to the "counter-clockwise" torque. Each object exerts a torque proportional to its weight and to its distance from the fulcrum.

You're right that the different distances change the answer. But the simple approach is right in the limit where the objects are much farther away from the fulcrum than they are from each other, and where the left and right objects are equally far away.

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