If a wire is stretched to double its length, its Young's modulus of elasticity will be

Question

Accepted Answer

Young's modulus of elasticity is a material property that measures the ability of a material to withstand changes in length when under lengthwise tension or compression. It is defined as the ratio of tensile stress (force per unit area) to tensile strain (proportional deformation in length).

1. **Explanation for Option 3 (Unchanged):**
   - Young's modulus is an intrinsic property of a material, meaning it is inherent to the material itself and does not depend on the shape or size of the material. It is determined by the material's atomic structure and bonding forces.
   - When a wire is stretched to double its length, the physical dimensions of the wire change, but the material's intrinsic properties, such as Young's modulus, remain constant. Therefore, the Young's modulus of elasticity remains unchanged regardless of the wire's length.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (Doubled):** Young's modulus is not dependent on the dimensions of the material. Doubling the length of the wire does not affect the atomic structure or bonding forces within the material, so Young's modulus does not double.
   - **Option 2 (Halved):** Similarly, halving the Young's modulus would imply a change in the material's intrinsic properties, which does not occur simply by stretching the wire. The modulus remains constant regardless of changes in length.
   - **Option 4 (Four times):** There is no basis for Young's modulus to increase fourfold due to a change in the wire's length. The modulus is a fundamental property of the material and remains constant irrespective of the wire's dimensions.

In conclusion, Young's modulus of elasticity is a fundamental property of the material itself and does not change with alterations in the wire's length. Therefore, Option 3 is the correct answer, as the Young's modulus remains unchanged when the wire is stretched.