Question

A steel wire is stretched by 1 kg-wt. If the radius of the wire is doubled, it's Young's modulus will
(A) Remains unchanged
(B) Becomes half
(C) Becomes double
(D) Becomes four times

Answer 1

Hint: In this question, we need to comment on the young modulus of elasticity of the material such that steel wire is stretched by 1 kg-wt. For this, we will follow the basic definition of the young modulus of elasticity of the material along with the properties.

Complete step by step answer:
-Stiffness of a solid material is denoted by the capital letter "E" and is expressed in the units of Pascal (P). In other words, it relates the tensile stress and the axial strain in the linear elastic region of a solid material. Young modulus is the ratio of the tensile strength and the axial strain developed on a solid material when an external force has been applied. Mathematically,
$E = \dfrac{\sigma }{\varepsilon }$
where, "E" is the young modulus of elasticity, $\sigma $ is the tensile strength of the solid material and $\varepsilon $ is the axial length of the solid material.
Moving further, the tensile strength of solid material is the ratio of the force applied per unit area of the solid material. Mathematically, $\sigma = \dfrac{F}{A}$ where $\sigma $ is the tensile strength of the solid material, "F" is the force applied on the area "A" of the base of the solid material.
-Also, the ratio of the change in the length of the solid material and the original length of the solid material on applying an external force results in the axial length of the solid material. Mathematically, $\varepsilon = \dfrac{{\vartriangle L}}{L}$ where $\varepsilon $ is the axial length of the solid material, $\vartriangle L$ is the change in the length and "L" is the initial length of the solid material.
-So, far we have discussed the details of the young modulus of the solid material and come to a conclusion that it is the property of the material which does not depend on the stress applied on the material and is specific for the materials.Hence, Young's modulus will remain unchanged when it is stretched by 1 kg-wt.
Hence,option A is correct.

Note:Young modulus of elasticity is the property of the material through which the geometrical shapes have been made. Moreover, students should know about the properties and the basic definition of the key terms involved in the question to answer these types of question.