A wooden wheel of radius $R$ is made of two semicircular parts (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 $\Delta T$ 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 Youngs' modulus is $Y$, the force that one part of the wheel applies on the other part is : <br>

Question

( A ) $2 S Y \alpha \Delta T$
( B ) $S Y \alpha \Delta T$
( C ) $\pi S Y \alpha \Delta T$
( D ) $2 \pi S Y \alpha \Delta T$