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A bimetallic strip is formed out of two ...

A bimetallic strip is formed out of two identical strips one of copper and the other of brass. The co-efficients of linear expansion of the two metals are `alpha_(C)` and `alpha_(B)`. On heating, the the strip bends to form an are of radius of curvature `R`. Then `R` is

A

proportional to `Delta `T

B

inversely proportional to `Detla `T

C

proportional to `|alpha_B -alpha_C| `

D

inversely proportional to` | alpha_B - alpha_C |`

Text Solution

Verified by Experts

The correct Answer is:
B, D
CO - efficient of linear expansion of brass is
greater than that of copper `i.e., alpha_B gt alpha_C`
` therefore L_B =L_0 ( 1 + alpha_B Delta T)`
`or (R +d ) theta = L_0 (1 + alpha_B Delta T)`
Again `L_C =L_0 (1 +alpha_C Delta T `
`or R theta = L_0 ( 1 + alpha_c Delta T )`
` therefore ((R +d ) theta)/( R theta) = (1 + alpha _B Delta T)/( 1 + alpha_C Delta T )`
`or (R +D )/(R ) =( 1 + alpha _B Delta T ) ( 1- alpha_c DeltaT)` by binomial theorem
` or 1+ d/R = 1 + ( alpha _B - alpha_C ) Delta T ` - Smaller terms
`or (d)/(R ) = (alpha_B - alpha_C ) Delta T or R= (d )/( ( alpha _B - alpha_C )Delta T )`
` therefore R prop (1)/( Delta T )` Option (b) is correct
and ` R prop (1)/(| alpha_s - alpha_c |)` option (d) is correct
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