If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

Solution

Physics sir · 4 steps

Young's modulus belongs to the material, not to the wire, so reshaping the wire cannot change it.

1. What Y measures. Young's modulus is the ratio of stress to strain, Y = (F/A)/(Δ L/L). It tells you how stiff the material is, like density or resistivity.

   Y = (F L)/(A Δ L)

2. Change the shape. Double L and halve r, so A = π r² becomes A/4. For the same load F, the extension changes to Δ L' = (F (2L))/((A/4) Y) = 8 Δ L.
3. Ratio stays fixed. The extension grows by exactly the factor needed to keep FL/(A Δ L) the same. Length and radius change how much the wire stretches, not Y.
4. So. The material is unchanged, so its Young's modulus remains the same: option (a).

The idea to keep. Y, like density and resistivity, is a property of the material. Changing length or thickness changes the extension and the stiffness of that wire, never Y itself.

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