Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has length 2l and diameter 2r. If the two wires are stretched by the same force, the elongation in A divided by elongation in B is
1/8
Stress=FA=F(πr24)
Strain developed =ΔLAl
young's modulus,Y=4Flπr2ΔLA
for wire B
Stress=FA=F(πr216)=16Fπr2
Strain=ΔLg2l
Y=2×16Flπr2ΔLB=32Flπr2ΔLB
Equating both [as both are of same material} ⇒4Flπr2ΔLA=32Flπr2ΔLB
⇒ΔLAΔLB=18