The Young's modulus of a wire of length L and radius r is Y N/m². If the length and radius are reduced to L/3 and r/4, then its Young's modulus will be

CONCEPT:

• Linear strain: If the deforming force produces a change in length alone, the strain produced in the body is called linear strain or tensile strain.

\(Linear\;strain = \frac{{change\;in\;length\;\left( {{\rm{\Delta }}l} \right)\;}}{{Original\;length\;\left( l \right)\;}}\)

• Stress: The internal restoring force acting per unit area of cross-section of the deformed body is called stress

\(Stress = \frac{{Force\;\left( F \right)}}{{Area\;\left( A \right)}}\)

• Young's Modulus (Y): It is defined as the ratio of normal stress to longitudinal strain within the limit of proportionality.

\(Y = \frac{{Normal\;stress}}{{longitudinal\;\;strain}} = \frac{{\frac{F}{A}}}{{\frac{{{\rm{\Delta }}l}}{l}}} = \frac{{Fl}}{{A{\rm{\Delta }}l}}\)

EXPLANATION:

• Its value depends upon the nature of the material of the body and the manner in which the body is deformed.
• Its value depends upon the temperature of the body.
• Its value is independent of the dimensions (length, radius, volume, etc.) of the body.
• As we know young's modulus of elasticity is a material's property. Therefore, Young's modulus does not depend upon the length of the radius of the wire. It is constant for the material.