TS EAMCET · Physics · Thermodynamics

A steel rod at $25 ° C$ is observed to be $1 m$ long when measured by another metal scale which is correct at $0 ° C$ . The exact length of steel rod at $0 ° C$ is $(α_{steel} = 12 \times 10^{- 6} ° C^{- 1}, α_{metal} = 20 \times 10^{- 6} ° C^{- 1})$

A $1.00002 m$
B $1.0002 m$
C $0.998 m$
D $0.9998 m$

Verified Solution

Answer & Solution

Correct Answer

(B) $1.0002 m$

Step-by-step Solution

Detailed explanation

Given: Length of steel rod at 25 °C is 1 m. The actual length measured by another metal scale at 25 °C is L=11+αm∆T L=11+25×20×10-6 ⇒L=1.0005 m this is the actual length measured by the other metal scale. Now, the steel…

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.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

A steel rod at 25°C is observed to be 1 m long when measured by another metal scale which is correct at 0°C. The exact length of steel rod at 0°C is αsteel=12×10-6 °C-1, αmetal=20×10-6 °C-1

Step-by-step Solution

A steel rod at $25 ° C$ is observed to be $1 m$ long when measured by another metal scale which is correct at $0 ° C$ . The exact length of steel rod at $0 ° C$ is $(α_{steel} = 12 \times 10^{- 6} ° C^{- 1}, α_{metal} = 20 \times 10^{- 6} ° C^{- 1})$