The young's modulus of a material is ` 2xx10 ^(11) N//m^2 ` and its elastic limit is ` 1xx10 ^(8) N//m ^2` for a wire of 1m length of this material , the maximum elongation achievable is

Options

A. `0.2 mm`
B. `0.3mm`
C. `0.4mm`
D. `0.5mm`

Answer

D

Explanation

Given ,
Young's modulus of material `= 2xx10 ^(11) N//m^2`
Elastic limit or stress `= 1 xx 10 ^(8) N// m^2`
Length of the wire = 1m
We know that
` Y = ( " Stress ")/(" Strain ") implies Y = ( " Stress ")/((Delta L)/(l))`
Here , l= original length of the wire
` Delta L=` charge in the length of the wire
` Delta L = ("Stress "xxl )/(Y ) = (1xx 10 ^8xx 1)/(2xx 10 ^(11))`
`0.5xx10 ^(-3)= 0.5 m m`