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Two bars are untressed and have lengths ...

Two bars are untressed and have lengths of `25cm` and `30cm` at `20^(@)C` as shown in Figure. Bar`(1)` is of aluminium and bar `(2)` is of steel. The croos-sectional area of bars are `20cm^(2)` for aluminium and `10cm^(2)` for steel. Assuming that the top and bottom supports are rigid, stress in `(N)/(mm^(2))` when the temperature is `70^(0)C`. (Nearly)
(`Y_(a)=0.70xx10^(5)N//mm^(2)Y_(s)=2.1xx10^(5)N//mm^(2).alpha_(a)=24xx10^(-6//0)C` and `alpha_(s)=12.xx10^(-6//0)C`)

A

`75, 150`

B

`25, 50`

C

`50, 100`

D

`100, 200`

Text Solution

Verified by Experts

The correct Answer is:
A
Contraction of the two bars due to compressive stress = Elongation of the two bars due to rise of temperature
`((Sl)/(Y))_(Al) + ((Sl)/(Y))_(St) = (alphaLDeltat)_(Al) + (alphaLDeltat)_(St)`
Force in steel `=` force in aluminium
`S_(Al) xx A_(Al) = S_(St) xx A_(St)`
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