A rod of length $$1000$$ mm and $$co-efficient$$ of linear expansion α $$=$$ $$10-4$$ per degree is placed symmetrically between fixed walls separated by $$l00l$$ mm. The Young's modulus of the rod is $$1011N/m2$$. If the temperature is increased by $$20$$°C, then the stress developed in the rod is (in$$ $$N/m2)

Question

A rod of length $$1000$$ mm and $$co-efficient$$ of linear expansion α $$=$$ $$10-4$$  per degree is placed symmetrically between fixed walls separated by $$l00l$$ mm. The Young's modulus of the rod is $$1011N/m2$$. If the temperature is increased by $$20$$°C, then the stress developed in the rod is (in$$ $$N/m2)

Infinity Learn · Accepted Answer

The change in length of rod due to increase in temperature in absence of walls is∆l $$=$$ lα ∆T $$=$$ $$1000$$×$$10-4$$×$$20$$ mm      $$=$$ $$2$$ mmBut the rod can expand upto $$1001$$ mm only.At that temperature its natural length is $$=$$ $$1002$$ mm.∴ compression $$=$$ l mm ∴  mechanical $$stress=$$ Y $$=$$ ∆ll $$=$$ $$1011$$×$$11000$$ $$=$$ $$108$$ $$N/m2$$

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A rod of length 1000 mm and co-efficient of linear expansion α = 10-4 per degree is placed symmetrically between fixed walls separated by l00l mm. The Young's modulus of the rod is 1011N/m2. If the temperature is increased by 20°C, then the stress developed in the rod is (in N/m2)

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