The force required to stretch a wire of cross-section 1 cm² to double its length will be : (Given Yong's modulus of the wire =2 × 10¹¹ N / m²)

Solution

Physics sir · 4 steps

Doubling the length means the extension equals the original length, so the strain is exactly 1.

1. Strain is 1. To double its length, the wire must stretch by Δ L = 2L - L = L. So the strain is (Δ L)/L = 1.

   F = Y A (Δ L)/L

2. Convert the area. A = 1 cm² = 1 × 10⁻⁴ m², because 1 cm = 10⁻² m and squaring gives 10⁻⁴.
3. Put in numbers. F = 2 × 10¹¹ × 1 × 10⁻⁴ × 1 = 2 × 10⁷ N.
4. So. The force needed is 2 × 10⁷ N, which is option (c).

The idea to keep. Doubling a length means strain = 1, so force = Y × A. Always convert the area to m² before you multiply.

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