When a metallic rod AB of length l = 1m, cross-sectional area 1 cm² and young's modulus $Y = 2 \times 10^{10} N / m^{2}$ is heated through a temperature of 20^oC, 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 20^oC, 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

Moderate

Solution

under the influence of compressive force, the deformation produced in the rod is, $δ = (2 - 1) mm = 1 mm$
Now, $\frac{F_{c} . l}{AY} = δ \Rightarrow F_{C} = \frac{AY δ_{}}{l} = \frac{10^{- 4} \times 2 \times 10^{10} \times 10^{- 3}}{1} N = 2000 N$

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