Nothing. Untill the two fingers touch each other. Try it!
It's all due to forces, distances, and friction. All you need
is to assume that the friction is depending on the pressure.
By the way, when the two fingers meet, you have found the
position of the center of mass of the broom!
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And here is a related question: if you cut the broom in two pieces
after the two fingers have met - right at the place they did -
which piece is heavier? Or are they perhaps of equal weight?
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