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A steel rod has a radius of 1 cm and a l...

A steel rod has a radius of 1 cm and a length of 1m. A 100 kN force stretches it along its length. Calculate (i) the stress, (ii) elongation and (iii) percentage strain on the rod. Given that young's modulus of elasticity for the steel rod `=2xx10^(11)N//m^(2)`.

Text Solution

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Here, area of cross-section of the rod `(A)=pi(10^(-2))^(2)m^(2)=10^(-4)pi=m^(2)`
Initial length `(l)=1m`
Force applied `(F)=100kN=10^(5)N`
Young's modulus `(Y)=2xx10^(11)N//m^(2)`.
`therefore` (i) Stress`=(F)/(A)=(10^(5))/((10^(-4)pi))=3.18xx10^(8)N//m^(2)`
(ii) Elongation=`Deltal=(F*L)/(AY)=(10^(5)xx1)/(10^(-4)pixx2xx10^(11))=1.59xx10^(-3)m`
(iii) Percentage strain`=(Deltal)/(l)xx100%=(1.59xx10^(-3))/(1)xx100%=1.59xx10^(-3)xx10^(-3)xx100%=0.159%`
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