A copper wire `(Y=10^(11) Nm^(-2))` of length 8 m and a steel wire `(Y=2xx10^(11) Nm^(-2))` of length 4 m, each of `0.5 cm^(2)` cross-section are fastened end to end and stretched with a tension of 500 N. choose the correct option.

Options

A. Elongation in copper wire is 0.8 mm
B. Elongation in steel is `(1)/(4)th` the elongation in copper wire.
C. Total elongation is 1.0 m
D. All of above

Answer

D

Explanation

(d) Elongation in the copper wire
`(Deltal)_(C)=((Fl)/(AY))_(C)=(500xx8)/(0.5xx10^(-4)xx10^(11))`

Elongation in the steel wire
`(Deltal)_(S)=((Fl)/(AY))=(500xx4)/(0.5xx10^(-4)xx2xx10^(11))`
`0.2xx10^(-3)m =0.2 mm`
`(Deltal)_(S)=(1)/(4)(Deltal)_(C)`
and total elongation `Deltal=0.8+ 0.2=1.0 mm`