Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount ?

Question

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δ l on applying a force F, how much force is needed to stretch the second wire by the same amount ? (A) F (B) 9 F (C) 4 F (D) 6 F

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/cad27104c6bf4c2025681b17f26aaebd-.png" /> For wire 1, Δ I = ((F/AY))3I ......(i) For wire 2, (F'/3A) = Y (Δ I/I) ⇒ Δ I = ((F'/3AY))I ....(iii) From equation (i) (ii), Δ I = ((F/AY)) 3I = ((F'/3AY))I ⇒ F' = 9F

F

9 F

4 F

6 F

For wire 1, ΔI=(AYF​)3I ......(i) For wire 2, 3AF′​=YIΔI​ ⇒ΔI=(3AYF′​)I ....(iii) From equation (i) & (ii), ΔI=(AYF​)3I=(3AYF′​)I ⇒F′=9F

For wire 1,
$Δ I = (\frac{F}{A Y}) 3 I$ ......(i)
For wire 2,
$\frac{F ^{'}}{3 A} = Y \frac{Δ I}{I}$
$\Rightarrow Δ I = (\frac{F ^{'}}{3 A Y}) I$ ....(iii)
From equation (i) & (ii),
$Δ I = (\frac{F}{A Y}) 3 I = (\frac{F ^{'}}{3 A Y}) I$
$\Rightarrow F^{'} = 9 F$