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

As we know that volume,
V = cross-sectional area A `xx` length `l`
`therefore V=Al`
Young's modulus, `Y=("Stress")/("Strain")`
`therefore` Work done, W
`=(1)/(2)xx"stress" xx "strain" xx "volume" `
or, `w=(1)/(2) xx Y xx ((Y)/(l))^(2)xxAl=(1)/(2)((YA)/(l))y^(2)`
or ` W prop y^(2)`