JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Heat & Thermodynamics

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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.
(

α_{iron} = 1.2 \times 1 0^{- 5} K^{- 1}

and

α_{brass} = 1.8 \times 1 0^{- 5} K^{- 1}

Answer: 60

Solution

For the difference in lengths to remain constant with temperature change:

ℓ_{B} (1 + α_{B} Δ T) - ℓ_{i} (1 + α_{i} Δ T) = ℓ_{B} - ℓ_{i}

. This simplifies to

α_{B} ℓ_{B} = α_{i} ℓ_{i}

. Substituting values:

1.8 \times 1 0^{- 5} \times 40 = 1.2 \times 1 0^{- 5} \times ℓ_{i}

. Solving:

ℓ_{i} = \frac{1.8 \times 40}{1.2} = \frac{72}{1.2} = 60

cm.

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Integer answer

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JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Heat & Thermodynamics

Solution

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