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

Options

A. y
B. `1//y`
C. `y^(2)`
D. `1//y^(2)`

Answer

C

Explanation

Volume V= cross-section area `A xx` length l or V= Al
Strain `= ("Elongation")/("Original length") = (Y)/(l)`
Young.s modulus, `Y = ("Stress")/("Strain")`
Work done, `W= (1)/(2) xx` stress `xx` strain `xx` volume
or `W= (1)/(2) xx Y xx ("strain")^(2) xx Al = (1)/(2) xx Y xx ((y)/(l))^(2) xx Al= (1)/(2) ((YA)/(l)) y^(2) or W prop y^(2)`