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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 2pi 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: |
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Answer» `2SY alpha DELTA T` `Y=((F)/(A))/((Delta L)/(L)) rArr (FL)/(A Delta L)` `rArr F=(Y A Delta L)/(L) =(Y A alpha L Delta T)/(L)` `rArr F= YA alpha Delta T rArr T =2 Y S alpha Delta T (because A=2S)` Correct choice : (a). |
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