A metallic rod of length l and cross – sectional area A is made of a material of Young’s modulus Y. If the rod is elongated by an amount y, then the work done is proportional to
Proportional refers to a relationship between two quantities where a change in one causes a corresponding change in the other. If two quantities are directly proportional, they increase or decrease together. Inversely proportional means one increases as the other decreases. This concept is widely used in physics and mathematics.
Class 11 Physics Chapter 8 explains the mechanical properties of solids. It includes topics like stress strain Hooke’s law elastic and plastic deformation Young’s modulus bulk modulus and shear modulus. The chapter focuses on the behavior of solids under forces and their deformation during stretching compressing bending and the factors influencing their elasticity.
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The work done (W) in elongating a rod is given by the formula:
W = 1/2 × Stress × Strain × Volume
Where:
– Stress = Force / Area
– Strain = ΔL / L (elongation per unit length)
As elongation, ΔL, is proportional to the applied force and Young’s modulus, work done is proportional to the square of the elongation.
Therefore, work done is proportional to y².
Check for more info:
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/