Question

The Young modulus of a rod length L and radius is Y. The rod is cut into two parts of equal length L/2 then young modulus of each part will be

Answer 1

Answer:

The Young modulus of each part will be Y.

Explanation:

The Young modulus of a solid material is defined as a measure of the stiffness of the material and it is given by the ratio of the stress to the strain of the material.

$\rm E = \dfrac{Stress}{Strain}.$

The stress is defined as the force per unit area of acting on the material.

$\rm Stress = \dfrac{F}{A}.$

The strain is defined as the deformation produced in the material which means the ratio of change in length $\rm \Delta L$ of the material to the orignal length $\rm L_o$ of the material.

$\rm Strain = \dfrac{\Delta L}{L_o}$.

Therefore,  

$\rm E = \dfrac{\dfrac{F}{A}}{\dfrac{\Delta L}{L_o}}=\dfrac{F\ L_o}{A\ \Delta L}.$

The Young modulus of a material does not depend on the dimensions of the body. It only varies with the stiffness of the material of the body.

Thus, the Young modulus of each part of the rod is still the same, i.e., Y.