l′s=l′b=5 m
Tf=400c
Actual length of brass tube, lb=?
Ti=0
For Length of scale at 00=ls, l′s=ls(1+αsΔT)
5=ls(1+40αs)
ls=51+40αs
Actual length of tube at 400
l′b=l′s+Δls
=l′s+l′s−ls
=2l′s−ls
l′b=(2×5−51+40αs)
Actual length of tube at 00c=lb
l′b=lb(1+α04T)
lb=l′b1+αb4T=(10−51+40αs)×11+40αb
=(10−51+40αs)×11+40αb
=(10−51+40×11×10−6)×(11+40×19×10−6)
=(10−51+440×10−6)×(11+760×10−6)
=(10−51.000440)×(11+00076)
=4.998≅4.999m
or
Let the length of tube and scale at 0oC be l. Then,
Change in measured tube length
Δl=Thermal expansion of brass− Thermal expansion of steel
Δl=lαBΔT−lΔαBΔT
Δl=lΔT(αB−αS)
Δl=l(40−0)(19×10−6−11×10−6)
So, new length measured by scale=l+Δl
⇒5=l+l(40)(7×10−6)
⇒51+40×7×10−6=l
⇒l=4.9986≈4.999m
Option C is correct.