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Two rods having length l1 and l2, made o...

Two rods having length `l_1` and `l_2`, made of materials with the linear expansion coefficient `alpha_1` and `alpha_2`, were soldered together. The equivalent coefficient of linear expansion for the obtained rod is

A

`(l_1alpha_2+l_2alpha_1)/(l_1+l_2)`

B

`(l_1alpha_1+l_2alpha_2)/(alpha_1+alpha_2)`

C

`(l_1alpha_1+l_2alpha_2)/(l_1+l_2)`

D

`(l_2alpha_1+l_1alpha_2)/(alpha_1+alpha_2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`L_1(1+alpha_1Deltat)+l_2(1+alpha_2Deltat)=l_f`
`l_f=l_1+l_2+(l_1alpha_1+l_2alpha_2)Deltat`
`l_f=l_1+l_2(1+(l_1alpha_1+l_2alpha_2)/(l_1+l_2))`
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