Question

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by Δ x on applying force F, how much force is needed to stretch wire 2 by the same amount?

• A. \(4F\)
• B. \(6F\)
• C. \(9F\)
• D. F

Hint:

For wires of same material and volume: Δ L ∝ (F)/(A²) Always use volume constraint to relate lengths.

Answer 1

The Correct Option is B

Step 1: Extension of a wire under force: Δ L = (FL)/(AY) where Y is Young’s modulus.
Step 2: Same material ⟹ Y same, and same volume: AL = 3A · L₂ ⟹ L₂ = (L)/(3)
Step 3: For same extension: (F L)/(A Y) = (F₂ L₂)/(3A Y)
Step 4: Substituting L₂=(L)/(3): (F L)/(A Y) = (F₂ L)/(9A Y) ⟹ F₂ = 6F