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Question:

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is:

0.25

4.00

0.50

2.00

Solution:

We have change in length Δl=F.l/YA
Since the two rods are in series (F1)rest=(F2)rest
Δl∝l/R²(∵A=πR²)
∴Δl1/Δl2=l1l2×R2²/R1²
Δl1/Δl2=2L/L×R²/4R²
Δl1/Δl2=1/2
∴Δl2/Δl1=2/1=2