When a wire is streched to duble its length

Options

A. strain is unity
B. stress is equal to Young's modulus of elasticity
C. its radius is halved
D. Young's modulus is equal to twice the elastic energy per unit volume

Answer

A, B, D

Explanation

(a) When the wire of length L is stretched to double its length, then increase in length `=2 L - L =L`.
`:. "Strain "=("increase in length")/("original length") =(L)/(L) =1`
(b) Young's modulus
`Y =("stress")/("strain") = ("stress")/(1) = stress`
(c) Initial volume = final volume `pi r^(2)(L) = pi r^('2)(2L)`
`r'=(r)/(sqrt(2))`
(d) `u=(U)/(Al)=(1)/(2)xxYxx("strain")^(2)`
`u=(1)/(2)xxYxx(1)^(2)` or `Y=2 u`