Under the same load, wire A having length 5.0 m and cross section 2.5 × 10⁻⁵ m² stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 × 10⁻⁵ m² stretches. The ratio of the Young's modulus of wire A to that of wire B will be :

Solution

Physics sir · 4 steps

Same load, same stretch, so Young's modulus depends only on length divided by area.

1. Write Young's modulus. Stress is F/A and strain is Δ L/L. Their ratio gives the modulus.

   Y = (F/A)/(Δ L/L) = (F L)/(A Δ L)

2. Cancel what is common. Both wires carry the same load F and stretch by the same Δ L. So Y ∝ L/A, and the ratio is Y_A/Y_B = (L_A/A_A)/(L_B/A_B).
3. Put in numbers. For A, 5.0/(2.5 × 10⁻⁵) = 2.0 × 10⁵ m⁻¹. For B, 6.0/(3.0 × 10⁻⁵) = 2.0 × 10⁵ m⁻¹.
4. So. The two values of L/A are equal, so Y_A : Y_B = 1 : 1, option (c).

The idea to keep. When load and extension are the same, cancel them first. Then Y ∝ L/A, and you only compare length over area for the two wires.

Answer from the NTA final answer key. Solution by PrepWiser.