Question

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 $a_C$ and $a_B$. On heating, the temperature of the strip goes $D_T$ and the strip bends to form an arc of radius of curvature R. Then R is

• A. Proportional to
• B. Inversely proportional to
• C. Proportional to
• D. Inversely proportional to

Answer 1

Answer: (B), (D)

The correct options are
B Inversely proportional to
D Inversely proportional to

Co-efficient of linear expansion of brass is greater than that of copper i.e ${\alpha }_B>{\alpha }_C\therefore L_B=L_0(1+{\alpha }_B\Delta T)or(R+d)\theta =L_0(1+{\alpha }_B\Delta T)Again,L_C=L_0(1+{\alpha }_C\Delta T)orR\theta =L_0(1+{\alpha }_C\Delta T)\therefore \frac{(R+d)\theta }{R\theta }=\frac{1+{\alpha }_B\Delta T}{1+{\alpha }_C\Delta T}$

$or\frac{R+d}{R}=(1+{\alpha }_B\Delta T)(1-{\alpha }_C\Delta T),bybinomialtheoremor1+\frac{d}{R}=1+({\alpha }_B-{\alpha }_C)\Delta T-Smallertermsor\frac{d}{R}=({\alpha }_B-{\alpha }_C)\Delta TorR=\frac{d}{({\alpha }_B-{\alpha }_C)\Delta T}\therefore R\propto \frac{1}{\Delta T}.Option\left(b\right)iscorrectandR\propto \frac{1}{|{\alpha }_B-{\alpha }_C|}.Option\left(d\right)iscorrect$