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Exam
NEET
Subject
Physics
Chapter
Thermal Properties of Matter

NEET · Physics · Thermal Properties of Matter

A composite rod is formed by joining a steel rod and a brass rod...

A composite rod is formed by joining a steel rod and a brass rod end-to-end. The total length of the composite rod is 100 cm100\text{ cm}. The effective coefficient of linear expansion of the composite rod is 1.4×10−5 K−11.4 \times 10^{-5}\text{ K}^{-1}. If the coefficients of linear expansion of steel and brass are 1.2×10−5 K−11.2 \times 10^{-5}\text{ K}^{-1} and 2.0×10−5 K−12.0 \times 10^{-5}\text{ K}^{-1} respectively, what is the length of the steel portion of the rod?

Options

  1. A25 cm25\text{ cm}
  2. B50 cm50\text{ cm}
  3. C75 cm75\text{ cm}
  4. D37.5 cm37.5\text{ cm}

Correct answer

C. 75 cm75\text{ cm}

Step-by-step solution

Let the length of the steel rod be LsL_s and the length of the brass rod be LbL_b.

The total length of the composite rod is L=Ls+Lb=100 cmL = L_s + L_b = 100\text{ cm}.

The total increase in length of the composite rod is the sum of the increases in length of the individual rods:
ΔL=ΔLs+ΔLb\Delta L = \Delta L_s + \Delta L_b

LαeffΔT=LsαsΔT+LbαbΔTL \alpha_{\text{eff}} \Delta T = L_s \alpha_s \Delta T + L_b \alpha_b \Delta T

Substituting the given values:
100×1.4×10−5=Ls×1.2×10−5+(100−Ls)×2.0×10−5100 \times 1.4 \times 10^{-5} = L_s \times 1.2 \times 10^{-5} + (100 - L_s) \times 2.0 \times 10^{-5}

Cancelling 10−510^{-5} from both sides:
140=1.2Ls+200−2.0Ls140 = 1.2 L_s + 200 - 2.0 L_s

0.8Ls=600.8 L_s = 60

Ls=600.8=75 cmL_s = \dfrac{60}{0.8} = 75\text{ cm}

Answer: 75 cm75\text{ cm}
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