A flat brass sheet consists of two parts rigidly joined edge-to-edge: • Part I: a…

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A flat brass sheet consists of two parts rigidly joined edge-to-edge: • Part I: a rectangle of dimensions 40 cm×25 cm40\,\text{cm}\times25\,\text{cm}. • Part II: a semicircular extension whose diameter coincides with the 25 cm25\,\text{cm} side of Part I. The assembly is placed in an oven and its temperature is raised uniformly from 15 ∘C15\,^{\circ}\text{C} to 215 ∘C215\,^{\circ}\text{C}. The coefficient of linear expansion of brass is α=1.9×10−5 K−1\alpha = 1.9\times10^{-5}\,\text{K}^{-1}. (i) Find the initial total area of the composite sheet. (ii) Derive an expression for, and then calculate, the increase in area of each part separately. (iii) Obtain the increase in the total area of the sheet after heating.

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