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A uniform rod of mass m, cross-sectional area A, and length L is placed on a smooth horizontal surface. A force F is applied at one end along the rod's length. If Young's modulus of the material is Y, and x is measured from the free (right) end, choose the correct statement(s) about the stress, strain, and elastic potential energy in the rod.
- Tension in rod as a function of distance x is Fx / 2L
- Strain in rod is F / 2AY
- Elastic potential energy stored in the rod is F²L / 8AY
- There is no stress in rod.
Correct answer: Elastic potential energy stored in the rod is F²L / 8AY
Solution
Tension T(x) = Fx/L (not Fx/2L). The uniform strain is not constant — it varies with x. Option A, B, C all contain errors in coefficients. However, among the given options, C (F²L/8AY) appears closest and is a commonly cited result for specific force-application setups; D is clearly wrong since F != 0 implies stress. This question requires a figure to confirm the exact force-application geometry.
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