Question

12.
The length of a steel rod (asteel = 12 x 10-6/°C) is measured by a brass metre scale
(Abrass = 18 × 10-6°C), when both of them are at 0°C, the steel rod measures 1.5 m. Find the
length of the rod as measured by the brass metre scale, when both of them are at 100°C.
Ans: 1.4991 m​

Answer 1

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)

⇒1+40×7×10−65=l

⇒l=4.9986≈4.999m

Option C is correct.