JEE Main202225 Jul 2022Morning ShiftPhysicsThermal Properties of MatterActual
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 × 10 - 5   K - 1 an
Correct answer
0
Step-by-step solution
Linear expansion of solid with temperature is given by L f = L 0 1 + α ∆ T Here, l B 1 + α B Δ T - l i 1 + α i Δ T = l B - l i ⇒ α B l B = l i α i ⇒ 1 . 8 × 10 - 5 × 40 = l i × 1 . 2 × 10 - 5 ⇒ l i = 1 . 8 × 10 - 5 × 40 1 . 2 × 10 - 5 = 3 × 40 2 = 60 ⇒ l i = 60   cm