A uniform rod of length L has a mass per unit length λ and area of cross section A. The…

Physics · JEE Advanced · NTA ExamsProperties of Solids and Liquids

A uniform rod of length L has a mass per unit length λ and area of cross section A. The elongation in the rod is due to its own weight if it is suspended from the ceiling of a room. The Young’s modulus of the rod is
  1. \(\frac{2 \lambda \mathrm{gL}^{2}}{\mathrm{~A} \ell}\)
  2. \(\frac{\lambda \mathrm{gL}^{2}}{2 \mathrm{~A} \ell}\)
  3. \(\frac{2 \lambda \mathrm{gL}}{\mathrm{~A} \ell}\)
  4. \(\frac{\lambda \mathrm{g} \ell^{2}}{\mathrm{AL}}\)

Answer

(B) gL ^ 2 2 ~A

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