JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 24)
A unit scale is to be prepared whose length does not change with temperature and remains $$20 \mathrm{~cm}$$, 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 $$40 \mathrm{~cm}$$ and length of iron will be __________ $$\mathrm{cm}$$. $$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right.$$ and $$\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} \mathrm{~K}^{-1}\right)$$.
Answer
60
Explanation
$$\Delta {L_1} = {\alpha _1}{L_1}\Delta T$$
$$\Delta {L_2} = {\alpha _2}{L_2}\Delta T$$
$${\alpha _1}{L_1} = {\alpha _2}{L_2}$$
$$1.2 \times {10^{ - 5}} \times {L_1} = 1.8 \times {10^{ - 5}} \times {L_2}$$
$${L_1} = {{1.8} \over {1.2}} \times 40 = 60$$ cm
Comments (0)
