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A steel rod with a cross-sectional area ...

A steel rod with a cross-sectional area of `150 mm^(2)` is stretched between two fixed points. The tensile load at `20^(@)C` is `5000N`.
`(a)` What will be the stress at `-20^(@)C` ?
`(b)` At what temperature will the stress be zero ?
(Assume `alpha=11.7mu m//m^(@)C` and `Y=200GN//m^(2)`)

A

`12.7 xx 10^(6) N//m^(2)`

B

`1.27 xx 10^(6) N//m^(2)`

C

`127 xx 10^(6) N//m^(2)`

D

`0.127 xx 10^(6) N//m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let L= free length at `0^(@)C`
`L_(0)` = final stretched length in each case. `L_(1) and L_(2)` are free lengths at `+20^(@)C and -20^(@)C`, respectively.

We know `delta_(2)= delta_(1) + 2alpha L Delta T`
Here, `s_(1) and s_(2)` are load deformation
`(F_(2)L)/(AY)= (F_(1)L)/(AY) + 2alpha L Delta T`
`sigma_(2)= (F_(2))/(A)= (F_(1))/(A) + 2 alpha Delta T Y`
`=(5000)/(150 xx10^(-6)) + (2) (11.7 xx 10^(-6)) (20) (2 xx 10^(11))`
`=127 xx 10^(6) N//m^(2)`
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