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A wooden wheel of radius  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  and length .  is slightly less than  To fit the ring on the wheel, it is heated so that its temperature rises by  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 , and its Young’s modulus is , the force that one part of the wheel applies on the other part is

a)

b)

c)

d)



Question ID - 56291 | SaraNextGen Top Answer

A wooden wheel of radius  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  and length .  is slightly less than  To fit the ring on the wheel, it is heated so that its temperature rises by  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 , and its Young’s modulus is , the force that one part of the wheel applies on the other part is

a)

b)

c)

d)

1 Answer
127 votes
Answer Key / Explanation : (d) -

(d)

If temperature increases by ,

Increase in length

Let tension developed in the ring is

 (From figure)

Where,  is the force that one part of the wheel applies on the other part

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