Question

Two identical thin metal strips, one of aluminum and the other of iron are riveted together to form a bimetallic strip. The temperature is raised by 50°C. If the central planes of the two strips are separated by 2 mm and the coefficients of thermal expansion for aluminum and iron are respectively 30 x 10^-6 / °C and 10 x 10^-6 / °C, the average radius of curvature of the bimetallic strip is about 

(a) 50 cm (b) 100 cm (c) 150 cm (d) 200 cm 

Answer 1

Correct option  (d) 200 cm 

Explanation:

For aluminum one can write  L_Al = L₀[1 + α_Alt] = R₂θ where R₂ is the radius of the arc of aluminum strip and t is the temperature. Note that θ is the angular width of the strips. A similar expression can be written for iron strip. The difference between the radii, say d, for aluminum and iron is the distance between the central planes of the two strips. The expression for d can be obtained from the above two expressions as  = L_0t[α_Al - α_Fe]/d .Also (R₁ + R₂) can be approximated as 2i and the value of R can be determined.