The correct option is A 80.0096 cm
Let the length of steel scale and copper wire at 20∘C be L0 .
For a change in temperature (ΔT), the length of a material changes to the new length given by, L=L0(1+α ΔT)
For steel scale,
New length due to change in temperature is given by
Lsteel=L0(1+αsteel ΔT) ......(1)
For copper wire,
New length due to change in temperature is given by
LCu=L0(1+αcu ΔT) ......(2)
The relative expansion of the copper wire w.r.t. steel scale after rise in temperature is given by
Lapp=LCu−Lsteel=[L0(1+αCuΔT)−L0(1+αsteelΔT)]
[ Using (1) and (2) ]
⇒Lapp=L0(αcu−αsteel)ΔT
Change in temperature (ΔT)=40−20=20∘C
⇒Lapp=80×(17×10−6−11×10−6)×20=0.0096 cm
Hence, the new length of the wire measured at 40∘ C
=L0+Lapp
=80.0096 cm
Hence, option (a) is the correct answer.