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JEE Main2012PhysicsThermal Properties of MatterActual

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 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

Options

  1. A2 S Y T
  2. BS Y T
  3. CS Y T
  4. D2 S Y T

Correct answer

D. 2 S Y T

Step-by-step solution

If temperature increases by T , Increase in length L , L = L T L L = T Let tension developed in the ring is T . T S = Y L L = Y T T = S Y T From FBD of one part of the wheel, F =2 T Where, F is the force that one part of the wheel applies on the other part. F =2 SY T

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