Fluid Statics: Practice Problem & Solution
The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length \(100 \text{cm}\) to stretch it by \(1 \text{mm}\) is (if Young's modulus of the wire \(= 2.0 \times 10^{11} \text{N} \text{m}^{-2}\)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Fluid Statics. Understanding the underlying formula is key to arriving at the correct answer below:
Energy density is \(u = \frac{1}{2} \times \text{Stress} \times \text{Strain} = \frac{1}{2} Y \left(\frac{\Delta l}{l}\right)^2 = \frac{1}{2} \times (2.0 \times 10^{11}) \times \left(\frac{10^{-3} \text{m}}{1 \text{m}}\right)^2 = 10^5 \text{J/m}^3\).
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