A bimetallic strip is formed out of two identical strips, one of copper and the other of brass. The coefficients of linear expansion of the two metals are `alpha_(c)` and `alpha_(B)`. On heating, the temperature of strip increases by `DeltaT` and the strip bends to form an arc of radius R. Then R is proportional to

Options

A. `DeltaT`
B. `1/(DeltaT)`
C. `sqrt(DeltaT)`
D. `1/sqrt(DeltaT)`

Answer

B

Explanation

Let,
Original length be l and lengths of brass and Copper be `l_(b)` and `l_(c)` respectively.
`l_(b)=l_(o)(1+alpha_(b)DeltaT) =(R+d)theta`
`l_(c)=l_(o)(1+alpha_(c)DeltaT)=Rtheta`
`(R+d)/R = (1+ alpha_(b)DeltaT)/(1+ alpha_(c)DeltaT)`
`implies 1 +d/R = 1+ (alpha_(a)-alpha_(b))DeltaT`
`impliesR=d/((alpha_(b)- alpha_(c))DeltaT)`
`therefore R propto 1/(DeltaT)`