Young's modules of material of a wire of length 'L' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

Solution

Physics sir · 4 steps

Young's modulus belongs to the material, not to the wire's shape, so reshaping the wire changes nothing.

1. What Y measures. Young's modulus is the ratio of stress to strain, Y = (F/A)/(Δ L/L) = FL/(A Δ L). It tells you how stiff the material is.
2. Change the shape. Doubling L and halving A changes how much this particular wire stretches under a given force. The extension becomes Δ L = FL/AY with 2L and A/2, so the same force now gives 4 times the extension.
3. Y stays put. Put those values back into the formula: F(2L)/(A/2)(4 Δ L) = FL/(A Δ L). The changes cancel, because Y depends only on what the wire is made of.
4. So. The material is unchanged, so Young's modulus is still Y. The answer is (d).

The idea to keep. Elastic moduli are material constants. Changing length or area changes the extension or the force constant YA/L, never Y itself. Only the material or the temperature can change it.

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