When a metallic rod AB of length l $$=$$ $$1m$$, $$cross-sectional$$ area $$1$$ $$cm2$$ and young's modulus $$Y=2$$×$$1010$$ $$N/m2$$ is heated through a temperature of $$20oC$$, its thermal expansion is found to be $$2$$ mm. Now the rod is cooled to its original temperature and placed between two walls as shown in the figure. The walls are not perfectly rigid. Now when the rod is heated through a temperature of $$20oC$$, the walls get deformed at the points of contact with the rod and increase in length of the rod is found to be $$1$$ mm. Then compressive force induced in the rod is

Question

When a metallic rod AB of length l $$=$$ $$1m$$, $$cross-sectional$$ area $$1$$ $$cm2$$ and young's modulus $$Y=2$$×$$1010$$ $$N/m2$$ is heated through a temperature of $$20oC$$, its thermal expansion is found to be $$2$$ mm. Now the rod is cooled to its original temperature and placed between two walls as shown in the figure. The walls are not perfectly rigid. Now when the rod is heated through a temperature of $$20oC$$, the walls get deformed at the points of contact with the rod and increase in length of the rod is found to be $$1$$ mm. Then compressive force induced in the rod is

Infinity Learn · Accepted Answer

under the influence of compressive force, the deformation produced in the rod is, δ$$=2$$−$$1mm=1$$ mmNow, Fc.$$lAY=$$δ⇒$$FC=AY$$δ $$l=10$$−$$4$$×$$2$$×$$1010$$×$$10-31N=2000$$ N

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