QJEEM12Ph34bb: JEE Main 2012 Physics - Class 11 JEEM12Ph34bb Solution: A wooden wheel of radius R is made of two semicircular part…

A wooden wheel of radius $$R$$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $$S$$ and length $$L.$$ $$L$$ is slightly less than $$2\pi R.$$ To fit the ring on the wheel, it is heated so that its temperature rises by $$\mathrm{\Delta }T$$ and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is $$\alpha$$, and its Young's modulus is $$Y,$$ the force that one part of the wheel applies on the other part is :