A wire of cross section 4 mm2 is stretched by 0.1 mm by a certain weight. How far (length) will the wire of same material and length but of area 8 mm2 stretch under the action of same force?

Question

A wire of cross section 4 mm2 is stretched by 0.1 mm by a certain weight. How far (length) will the wire of same material and length but of area 8 mm2 stretch under the action of same force? (A) 0.05 mm (B) 0.10 mm (C) 0.15 mm (D) 0.20 mm

Tardigrade Admin · Accepted Answer

Given A1 = 4 mm2 = 4 × 10-6 m2, Δ L1=0.1 ×10-3 m, A2 =8 ×10-6 m2, Y2 = Y1, L2=L1,F2=F1 Δ L1=(F1 L1/A1Y1),Δ L2 = (F2L2/A2Y2) (Δ L2/Δ L1)= (A1/A2)=(4 ×10-6/8×10-6)=(1/2) ∴ Δ L2 =(Δ L1/2) = 0.05 × 10-3 m = 0.05 mm

Q. A wire of cross section 4mm2 is stretched by 0.1mm by a certain weight. How far (length) will the wire of same material and length but of area 8mm2 stretch under the action of same force?

0.05 mm

0.10 mm

0.15 mm

0.20 mm

Given A1​=4mm2=4×10−6m2, ΔL1​=0.1×10−3m,A2​=8×10−6m2, Y2​=Y1​,L2​=L1​,F2​=F1​ ΔL1​=A1​Y1​F1​L1​​,ΔL2​=A2​Y2​F2​L2​​ ΔL1​ΔL2​​=A2​A1​​=8×10−64×10−6​=21​ ∴ΔL2​=2ΔL1​​=0.05×10−3m=0.05mm

Q. A wire of cross section $4 m m^{2}$ is stretched by $0.1 mm$ by a certain weight. How far (length) will the wire of same material and length but of area $8 m m^{2}$ stretch under the action of same force?