A uniform heavy rod of weight 10 kg , cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young's modulus of the material of the rod is 2×1011Nm−2 . Neglecting the lateral contraction, the elongation of rod due to its own weight is ……x 10-9m (take g=10ms-2)

y=dmg xAΔl dm=ml=dx Δl=mgAly(x22)0l∆l=WL2AY=5×10-9 m

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A uniform heavy rod of weight 10 kg , cross-sectional area 100 $c m^{2}$ and length 20 cm is hanging from a fixed support. Young's modulus of the material of the rod is $2 \times 10^{11} N m^{- 2}$ . Neglecting the lateral contraction, the elongation of rod due to its own weight is ……x 10^-9m (take g=10ms^-2)

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$y = \frac{d_{m} g x}{A Δ l} d_{m} = \frac{m}{l} = d x Δ l = \frac{m g}{A l y} {(\frac{x^{2}}{2})}_{0}^{l}$

$∆ l = \frac{W L}{2 A Y} = 5 \times 10^{- 9} m$

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