1st Case: For cast iron 2nd Case: For Al
F = 6.5 × 103 N F = 6.5 × 103 N
l = 1.3 m l = 2.6 m
r = 0.2 × 10-2 m ⇒ A = 0.04π × 10-4 m2 A = 0.04π × 10-4 m2
Y = 100 × 1010 N/m2 Y = 7 × 1010 N/m2
Now, formula of Young's modulus is
Y=12FlA△l △l2=12FLAY
⇒△l1=12FLAY =12×6.5×103×2.60.04π×10−4×7×1010
=12×6.5×103×1.30.04π×10−4×100×1010
In order to get the elongation of the whole rod, calculate △l1 and △l2 separately and add them.
∴ Elongation of rod = △l1 + △l2
I hope its clear :)