A long wire is stretched by 0.2 cm and energy density is 0.25 J `m^(-3)`, what will be the energy density when stretched by 1 cm ?

Options

A. `1/100Jm^(-3)`
B. `1/20Jm^(-3)`
C. `5/4Jm^(-3)`
D. `25/4Jm^(-3)`

Answer

D

Explanation

Energy density=`1/2Y("Strain")^(2)`
`Uprop("extension")^(2)`
`U_(1)=0.25Jm^(-3)`
`l_(1)=0.2cm,l_(2)=1cm`
`(U_(2))/(U_(2))=((l_(2)^(2))/(l_(2)^(1)))=1/((0.2)^(2))=100/4=25`
`U_(2)=254U_(1)=25xx0.25=25/4`
Correct choice is (d).