A unit scale is to be prepared whose length does not change with … - Vidyadip

MCQ

A unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40\,cm$ and length of iron will be$...cm$

$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.$ and $\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)$.

A
$59$
B
$6$
✓
$60$
D
$600$

✓

Answer

Correct option: C.

$60$

c
$\ell_{ B }\left(1+\alpha_{ B } \Delta T \right)-\ell_{ i }\left(1+\alpha_{ i } \Delta T \right)=\ell_{ B }-\ell_{ i }$

$\alpha_{ B } \ell_{ B }=\ell_{ i } \alpha_{ i }$

$1.8 \times 10^{-5} \times 40=\ell_{ i } \times 1.2 \times 10^{-5}$

$\ell_{ i }=\frac{1.8 \times 10^{-5} \times 40}{1.2 \times 10^{-5}}=\frac{3 \times 40}{2}=60$ $\ell_{ i }=60\,cm$

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