JEE Physics 2024 Question with Solution

Given: Young’s modulus of the material is $Y$ for a wire of length $L$ and cross-sectional area $A$.

Find: Young’s modulus when the length becomes $2L$ and the cross-sectional area becomes $\frac{A}{2}$.

Young's modulus is defined as

It is a property of the material and does not depend on the dimensions of the wire, provided the material remains the same and deformation is within the elastic limit.

So, even if the length is doubled and the cross-sectional area is halved, the value of Young’s modulus remains unchanged.

Therefore, the Young’s modulus is $Y$. The solution working gives the final value as $Y$, although the solution labels the correct option as C. Based on the solution explanation, the defensible option is B.

Given: Same material, but wire dimensions are changed.

Find: Whether Young’s modulus changes with geometry.

Young’s modulus relates stress to strain:

Although $L$ and $A$ appear in the formula, they are part of the measured deformation relation for a specimen. For a given material, the ratio of stress to strain remains fixed in the elastic region.

Hence changing the wire length from $L$ to $2L$ and area from $A$ to $\frac{A}{2}$ does not change the material constant.

Therefore, the correct option is B.