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A wooden wheel of radius R is made of tw...

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 whell, 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 semicirular parts together. If te doefficient of linear expansion of the metal is `alpha`, and its Youngs' modulus is dY, the force that on part of the wheel applies on the other part is :

A

`2pi S Y alpha DeltaT`

B

`Sy alpha Delta T`

C

`piSY alpha DeltaT`

D

`2S Y alpha DeltaT`

Text Solution

Verified by Experts

The correct Answer is:
D

`L rArr S`
`DeltaL = L prop DeltaT`
`(F)/(A) = (DeltaL)/(L)Y`
`F = alpha DeltaT Y S`
So, `T = 2F`
`T =2 alpha DeltaT Y S`
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