A wooden wheel of radius $R$ is made of two semicircular parts. 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 $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses 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:

1. A
   $2\pi SY\alpha \Delta T$
2. B
   $SY\alpha \Delta T$
3. C
   $\pi SY\alpha \Delta T$
4. D
   $2SY\alpha \Delta T$