The 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
Text Solution
Verified by ExpertsD
Elongation due to change in temperature,
… (i)
where, 
coefficient of linear expansion,
which is compensated by elastic strain.
When temperature becomes normal, then
… (ii)
From Eqs. (i) and (ii), we get
At equilibrium, force exerted by one-half on other,
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