Question

Rigidity modulus of steel is $\eta$ and Young's modulus is $Y$. A piece of steel of cross-sectional area ‘$A$’ is changed into a wire of length $L$ and area $A/10$ then:
A. $Y$ increase and $\eta$ decrease
B. $Y$ and $\eta$ remains the same
C. both $Y$ and $\eta$ increase
D. both $Y$ and $\eta$ decrease

Answer 1

Recall the basics of Young’s modulus and modulus of rigidity of the material of a substance. From the basic information about these physical quantities, check whether these two physical quantities depend on the dimensions and geometry of the material and if it depends what is the relation between them.

Complete step by step answer:
We have given that the modulus of rigidity is $\eta$ and the Young’s modulus is $Y$.
A piece of steel of cross-sectional area ‘$A$’ is changed into a wire of length $L$ and area $A/10$.
We know that when the piece of steel of cross-sectional area ‘$A$’ is changed into a wire of length $L$ and area $A/10$ then the dimensions and geometry of the steel piece changes.
But the Young’s modulus $Y$ and modulus of rigidity $\eta$ for a material are constant and do not change with change in dimensions and geometry of the material.
Therefore, although the piece of steel is changed into wire of a different area than the area of the piece of steel, the Young’s modulus and modulus of rigidity of the steel material remains the same.

So, the correct answer is “Option B”.

Note:
The students may get confused that the Young’s modulus and modulus of rigidity of the steel should change when the geometry and dimensions of the piece of steel are changed according to the formulae for these two constants. But the physical quantities in the formulae of these two constant changes such that the final value of Young’s modulus and modulus of rigidity of the steel remains the same.