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Two wires A and B are made of the same material. Wire A has twice the diameter and three times the length of wire B. Within the elastic limit, both are stretched by the same tension. Find the ratio of the elastic potential energy stored in A to that in B.

1. 2: 3
2. 3: 4
3. 3: 2
4. 6: 1

Correct answer: 3: 4

Solution

Since U is proportional to F²*L/(A*Y) and F, Y are the same, U scales as L/A; with A four times larger and L three times larger for wire A, U_A/U_B = 3/4.

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