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    Question

    Two wires made of the same material have lengths in the

    ratio 1:2 and diameters in the ratio 2:1. If the same force is applied to both, what is the ratio of work done (elastic potential energy) stored in the shorter to longer wire?
    A 1:4 Correct Answer Incorrect Answer
    B 4:1 Correct Answer Incorrect Answer
    C 1:8 Correct Answer Incorrect Answer
    D 8:1 Correct Answer Incorrect Answer

    Solution

    The work done (or elastic potential energy ) stored in a stretched wire is given by: Where:

    • F is the force applied,
    • L is the length of the wire,
    • A is the cross-sectional area,
    • Y is Young’s modulus (same material ⇒ same Y).
    We are comparing two wires :
    • Lengths in the ratio: L1:L2 = 1:2
    • Diameters in the ratio: d1:d2 = 2:1
    So, areas  So, energy stored in the shorter wire is 1/8 of that in the longer wire.

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