Three springs, labelled (A), (B) and (C) are arranged as shown with three identical balls all the springs are parts cut from a single long spring such that A and B have equal natural length $ℓ$ but C has natural length $2 ℓ$ . All surfaces are smooth. Which spring is compressed by the smallest amount in equilibrium?

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All three springs are cut from the same long spring. Springs A and B each have natural length $ℓ$ and spring constant $k$ ; C has natural length $2 ℓ$ , so its spring constant is $k /2$ .

A supports one ball: compression $\frac{m g}{k}$ . B supports two balls: $\frac{2 m g}{k}$ . C supports one ball: $\frac{m g}{k /2} = \frac{2 m g}{k}$ .

The smallest compression is in spring A.

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