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Two rods ' A ' & ' B ' of equal free len...

Two rods `' A '` & `' B '` of equal free length hang vertically `60 cm` apart and support a rigid bar horizontally. The bar remains horizontal when carrying a load of `5000 kg` at `20 cm` from `'A'`. If the stress in `'B'` is `50 N//mm^(2)`m, find the stress in `'A'` and the areas of `'A'` and `'B'`
Given `Y_(B) = 9 xx 10^(4) N//m^(2),Y_(A) = 2 xx 10^(5) N//mm^(2), g = 10m//sec^(2)`

Text Solution

Verified by Experts

The correct Answer is:
`(1000)/(9) N//mm^(2) , 300 mm^(2) , (1000)/(3)mm^(2)`
`Y_(A) = 2 xx 10^(5) N//mm^(2)`
`Y_(B) = 9 xx 10^(4) N//mm^(2)`
`F_(A) xx 20 = F_(B) xx 40`
`F_(A) = 2F_(B)`
`F_(A) + F_(B) = 5000 g`
`F_(B) = (5000)/(3), F_(A) = (10000g)/(3)`
`sigma_(B) = 50 = (F_(B))/(A_(B)), A_(B) = (50 xx 10^(3))/(3 xx 50) = (1000)/(3)mm^(2)`
`Deltal = (F_(B)l)/(A_(B)Y_(B)) = (F_(A)l)/(A_(A)Y_(A)), sigma_(A) = (F_(A))/(A_(A)) = (Y_(A))/(Y_(B)) sigma_(B) = (20)/(9) xx 50 = (1000)/(9) N//mm^(2)`
`sigma_(A) = (1000)/(9) = (10^(5))/(3A_(A)), A_(A) = 300 mm^(2)`
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