AP EAMCET · PHYSICS · Thermal Properties of Matter

A metal tape is calibrated at $25 ° C$ . On a cold day when the temperature is $- 15 ° C$ , the percentage error in the measurement of length is
(Coefficient of linear expansion of metal $= 1 \times 10^{- 5} {}^{\circ}C^{- 1}$ )

A $0.04 %$
B $0.05 %$
C $0.1 %$
D $0.08 %$

Verified Solution

Answer & Solution

Correct Answer

(A) $0.04 %$

Step-by-step Solution

Detailed explanation

Length of the steel tape can be written as,L=L01+α(T-25°) Now, percentage error in measurement can be written as, ∆LL×100%=α(T-25°)×100=1×10-5-15°-25°×100=0.04%

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A metal tape is calibrated at 25°C. On a cold day when the temperature is -15°C, the percentage error in the measurement of length is(Coefficient of linear expansion of metal =1×10-5C-1∘)

Step-by-step Solution

A metal tape is calibrated at $25 ° C$ . On a cold day when the temperature is $- 15 ° C$ , the percentage error in the measurement of length is
(Coefficient of linear expansion of metal $= 1 \times 10^{- 5} {}^{\circ}C^{- 1}$ )