A wooden wheel of radius R is made of two semicircular parts (as in 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$\mathrm{\pi }$R . To fit the ring on the wheel, it is heated so that its temperature rises by $∆$T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the co-efficient of linear expansion of the metal is $\alpha$ and its Young's modulus y then, the force that one part of the wheel applies on the other part is