In the Young’s experiment, if length of wire and radius both are doubled then the value of Y will become

The correct option/answer is: Remains same.

Step-by-Step Explanation:

1. Understanding Young's Modulus:
Young's modulus ($Y$) is a fundamental mechanical property of a solid material. It measures the tensile stiffness of a material and is defined as the ratio of tensile stress ($\sigma$) to tensile strain ($\epsilon$) in the linear elastic region:
$Y=\frac{\text{Stress}}{\text{Strain}}$

2. Material Property vs. Dimensions:
Young's modulus ($Y$) depends solely on the nature of the material of the wire (such as steel, copper, or aluminum) and its temperature.
It is an intensive property, which means it does not depend on the physical dimensions of the specimen, such as the length ($L$) or the radius ($r$) of the wire.

3. Effect of Doubling Dimensions:
Even if the length ($L$) is doubled to $2L$ and the radius ($r$) is doubled to $2r$, the chemical composition and material of the wire remain exactly the same.
Therefore, the value of Young's modulus ($Y$) remains unchanged.