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Question

A bimetallic strip on heating has radius R. The coefficients of thermal expansion are α1 and α2. If the strip having greater coefficient of thermal expansion (α1) is replaced by an identical strip having coefficient of thermal expansion 3 times its value (i.e 3α1) and heated to the same temperature difference, then the new radius of the arc is
[ given, α1α2=2 ]

A
R5
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B
2R
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C
5R
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D
R2
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Solution

The correct option is A R5
Given:
Radius of metallic strip =R
Coefficient of linear expansion of strip 1 =α1
Coefficient of linear expansion of strip 2 =α2
Coefficient of linear expansion of strip 3 with which strip 1 is replaced, α3=3α1
Given: α1α2=2
To find:
New radius of arc of bimetallic strip, R=?
Let us suppose:
Temperature change =ΔT
Thickness of each strip =t

We know that, radius of arc of the bimetallic strip is given by
R=t(α1α2)ΔT
R=tα2ΔT .......(1)
[ given, α1=2α2 ]
Now, after replacing strip 1 with strip 3,
R=t(α3α2)ΔT
R=t5α2ΔT ......(2)
[ given, α3=3α1 and α1=2α2 ]
From (1) and (2)
R=R5

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