Heat and Thermal ExpansionHard
Question
A wooden wheel of radius R is made of twosemicircular parts (see figure). The two partsare held together by a ring made of a metal stripof cross sectional area S and Length L. L isslightly less than 
. To fit the ring on the wheel, it is heated so that its temperature rises by ᐃT and it just steps over the wheel. As it coolsdown to surrounding temperature, it presses thesemicircular parts together. If the coefficient oflinear expansion of the metal is α, and itsYoung′s modulus is Y, the force that one partof the wheel applies on the other part is :
. To fit the ring on the wheel, it is heated so that its temperature rises by ᐃT and it just steps over the wheel. As it coolsdown to surrounding temperature, it presses thesemicircular parts together. If the coefficient oflinear expansion of the metal is α, and itsYoung′s modulus is Y, the force that one partof the wheel applies on the other part is :Options
A.2SYαᐃT
B.2 π SYαᐃT
C.SY αᐃT
D.πSY αᐃT
Solution
⇒ stress = Y × strain
⇒ F = SY αᐃT Therefore force by one part on other part
= 2F = 2SYαᐃT
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