question_answer

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 Young's modulus is Y, the force that one part of the wheel applies on the other part is:          [AIEEE 2012]

A)  \[2\pi SY\alpha \Delta T\]           

B)       \[SY\alpha \,\Delta T\]

C)  \[\pi SY\alpha \,\Delta T\]          

D)       \[2SY\alpha \,\Delta T\]

Correct Answer: D

Solution :

[d]

So,