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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

A steel tape measures the length of a copper rod as 90. 0cm when...

A steel tape measures the length of a copper rod as 90.0cm90. 0cm when both are at 10°C10 ° C, the calibration temperature for the tape. What would be the tape reading for the length of the rod when both are at 30°C30 ° C. Given, α\alpha for steel1.2×10−5°C−11.2 \times {10}^{- 5} ° C^{- 1} and α\alpha for copper is1.7×10−5°C−1.1.7 \times {10}^{- 5} ° C^{- 1}.

Options

  1. A90.01cm90. 01cm
  2. B89.90cm89. 90cm
  3. C90.22cm90. 22cm
  4. D89.80cm89. 80cm

Correct answer

A. 90.01cm90. 01cm

Step-by-step solution

As the steel tape is calibrated at 10°C10 ° C, therefore, adjacent centimeter marks on the steel tape will be separated by a distance of

lt=l10(1+αs∆T)=(1+αs20){l}_{t} = {l}_{10}\left(1 + {\alpha}_{s} ∆ T\right) = ( 1 + {\alpha}_{s}20 ) cm

Length of copper rod at 30°C30 ° C

= 90(1+αc20)90 \left(1 + {\alpha}_{c}20\right) cm

Therefore, number of centimeters read on the tape will be

= 90(1+αc20)1(1+αs20)=90(1+1.7×10−5×20)1(1+1.2×10−5×20)\dfrac{90\left(1 + {\alpha}_{c}20\right)}{1\left(1 + {\alpha}_{s}20\right)} = \dfrac{90\left(1 + 1.7 \times {10}^{- 5} \times 20\right)}{1\left(1 + 1.2 \times {10}^{- 5} \times 20\right)}

= 90×1.000341.00024=\dfrac{90 \times 1.00034}{1.00024} =90.01cmcm
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