#### Q. A brass rod of length 50 cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250^{0}C, if the original lengths are at 40^{0}C? Coefficient of linear expansion of brass and steel are 2.1 × 10^{-5} ^{0}C^{-1} and 1.2 × 10^{-5} ^{0}C^{-1} respectively) (CBSE)

Aditya Bhatt Answered question 25 January 2024

Best Solution:-

Initial temperature, T1=40oC

Final temperature, T2=250oC

Change in temperature, △T=T2−T1=2100C

For the expansion in the **Brass rod**, we have:

Change in length (△l1) / Original length (l1) = α1△T

∴△l1 = 50 × (2.1×10−5) × 210

= 0.2205cm

For the expansion in the **steel rod**, we have:

Change in length (△l2)/ Original length (l2) = α2△T

∴△l1 = 50 × (1.2×10−5) × 210

=0.126cm

Total change in the lengths of brass and steel,

**△****l =****△****l1 + ****△****l2**

=0.2205 + 0.126

=**0.346cm**

Total change in the length of the combined rod =**0.346cm**

Since the rod expands freely from both ends, no thermal stress is developed at the junction.

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Aditya Bhatt Answered question 25 January 2024