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A brass rod of length 50cm

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 2500C, if the original lengths are at 400C? Coefficient of linear expansion of brass and steel are 2.1 × 10-5 0C-1 and 1.2 × 10-5 0C-1 respectively)                                                               (CBSE)

Aditya Bhatt Answered question 25 January 2024
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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.

 

Aditya Bhatt Answered question 25 January 2024
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