Final answer:
Young's modulus is a property that depends on the material itself and does not change when the geometry of the object is altered. Thus, reducing the length and radius of the wire will not change its Young's modulus.
Step-by-step explanation:
The Young's modulus of a material is an intrinsic property that measures its stiffness and is represented by the symbol Y. It does not depend on the geometry of the material, such as its length or cross-sectional area, but rather on the material's own properties.
Therefore, if you change the dimensions of the wire, specifically reducing the length to L/2 and the radius to r/4, the Young's modulus will remain unchanged as it is a property of the material itself and is independent of its size or shape.
Young's modulus (Y) of a wire is a property of the material that measures its stiffness or elasticity. It depends on the substance, cross-sectional area (A), and original length (Lo) of the wire.
When the length of the wire is reduced to L/2 and the radius is reduced to r/4, the new Young's modulus (Y') can be calculated using the formula:
Y' = (Y * A') / (A * L')
where A' is the new cross-sectional area which is given by (π * (r/4)^2) and L' is the new length which is L/2