Ncert Exercises & Solutions

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that the difference between their length B remains constant. If $α_{i r o n} = 1.2 \times 10^{- 5} / K a n d α_{b r a s s} = 1.8 \times 10^{- 5} / K,$ what should we take as the length of each strip?

Hint: The difference of length of each strip should remain the same.

Step 1: Find the change in length of each strip.

According to question,

l_{i r o n} - l_{b r a s s}

= 10 cm=constant at all temperatures

Let

l_{0}

be length at temperature 0°C and l be the length after change in temperature of

∆

Now, we can write,

l_{i r o n} - l_{b r a s s}

= 10 cm at all temperatures

l_{i r o n} (1 + α_{i r o n} ∆ T) - l_{b r a s s} (1 + α_{b r a s s} ∆ T) = 10 c m

l_{i r o n} α_{i r o n} = l_{b r a s s} α_{b r a s s}

Step 2: Find the length of each strip.

∴ \frac{l_{i r o n}}{l_{b r a s s}} = \frac{1.8}{1.2} = \frac{3}{2}

∴ \frac{1}{2} l_{b r a s s} = 10 c m

\Rightarrow l_{b r a s s} = 20 C M a n d l_{i r o n} 30 C M

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