Young's modulus of a uniform cross section rod, linearly varries from $Y_{0}$ (end A) to $2 Y_{0}$ (end B). Two equal forces are acting at ends of rod (area of cross-section $= A$ , length $= ℓ$ )

Question

Young's modulus of a uniform cross section rod, linearly varries from Y 0 ​ (end A) to 2 Y 0 ​ (end B). Two equal forces are acting at ends of rod (area of cross-section = A , length = ℓ )

TestHub · Accepted Answer

stress is A F ​ , ∴ it will be same at all points. Young's modulus on element dx will be Y 0 ​ + L Y 0 ​ ​ x let extension in dx be dy ​ then A F ​ = ( Y 0 ​ + L Y 0 ​ x ​ ) d x d y ​ ​ ∫ Δ L L ​ A F L ​ ( Y 0 ​ L + Y 0 ​ x ) d x ​ = ∫ 0 0 ​ d y ​ Δ L : total alongation in rod. ​

Physics - Elasticity Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion