Question

The temperature of a body shown by a faulty Celsius thermometer is 49 °C and by a correct Fahrenheit thermometer is 122 °F. The correction to be applied to the faulty thermometer is

• A. -12 °C
• B. +1 °C
• C. +12 °C
• D. -1 °C

Hint:

Distinguish between "error" and "correction". Error is how much the measurement is off (\(\text{True} - \text{Measured}\)). Correction is what you must add to the measurement to fix it (\(\text{Correction} = -\text{Error}\)). In this case, the error is -1°C (it reads 1°C too low), so the correction is +1°C.

Answer 1

The Correct Option is B

To find the correction needed for the faulty Celsius thermometer, we need to compare the given temperature readings on both scales and determine the error.

The problem states that:

• The faulty Celsius thermometer reads \(49^\circ\text{C}\).
• The correct Fahrenheit thermometer reads \(122^\circ\text{F}\).

First, we need to convert the correct Fahrenheit reading to Celsius to see what the correct Celsius temperature is.

Step 1: Convert Fahrenheit to Celsius.

We use the formula to convert Fahrenheit to Celsius:

\(C = \frac{5}{9}(F - 32)\)

Substituting the given Fahrenheit temperature:

\(C = \frac{5}{9}(122 - 32)\)

\(C = \frac{5}{9}(90)\)

\(C = 50^\circ\text{C}\)

Step 2: Determine the Correction Needed.

The correct Celsius reading should be \(50^\circ\text{C}\). However, the faulty thermometer shows \(49^\circ\text{C}\).

The correction needed is:

\(50 - 49 = 1^\circ\text{C}\)

Conclusion

The correction to be applied to the faulty thermometer is \(+1^\circ\text{C}\). Therefore, the correct answer is +1 °C.