spring constant and modulus q

Could someone please double check my logic for question 3c?
https://pmt.physicsandmathstutor.com/download/Admissions/ENGAA/Papers/ENGAA%202017%20Section%202.pdf

k ∝ A/L, where k is spring constant, A is cross sectional area, and L is length.
so if L halves, then k doubles.

then using young modulus equation, E = FL/AX, where E is young modulus, F is force, X is extension
if L halves, then since F and A are constant, X must halve.

Energy equation = 1/2 * k * X^2, so if k doubles and X halves, the energy must halve.

so its U/2 = 1/2mv^2, thus answer is B

Reply 1

lordaxil

Your logic is correct, but you could have arrived at same answer more directly by saying the cord is half the size so it must have half of the energy at maximum strain.

Reply 2

Kallisto

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Original post by mosaurlodon

I see no mistakes in your logic. When you have one or more constants, you need to change the alterable units in equations in the same amount to balance them, as they are proportional to each other. In your cases:

E ~ X (for F and A constants)
Energy ~ X (for k constant)