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 mm
D. All of the above

Answer

d

Explanation

`(Delta I)_(c ) = ((FI)/(AY))_(c ) = (500 xx 8)/(0.5 xx 10^(-4) xx 10^(11))`

`= 0.8 xx 10^(-3) m = 0.8 mm`
`(Delta I)_(s) = ((FI)/(Ay))_(S) = (500 xx 4)/(0.5 xx 10^(-4) xx 2 xx 10^(11))`
`0.2 xx 10^(-3) m = 0.2 mm`
`(Delta I)_(s) = (1)/(4) (DeltaI)_(c )`
and `Delta I = 0.8 _ 0,2 = 1.0 mm`