Students A, B and C measure the length of a room using 25 m long measuring tape of least count (LC) 0.5 cm, meter-scale of LC 0.1 cm and a foot-scale of LC 0.05 cm, respectively. If the specified length of the room is 9.5 m, then which of the following students will report the lowest relative error in the measured length ?

Options

A. Student A
B. Student B
C. Student C
D. Both, student B and C

Explanation

To determine which student reports the lowest relative error in measuring the length of the room, we will calculate the relative error for each student based on the least count of their measuring instruments.

### Step-by-Step Solution:

1. **Identify the Least Count for Each Student:**
- Student A uses a measuring tape with a least count (LC) of 0.5 cm.
- Student B uses a meter scale with a least count (LC) of 0.1 cm.
- Student C uses a foot scale with a least count (LC) of 0.05 cm.

2. **Convert the Least Counts to Meters:**
- Student A: \( LC_A = 0.5 \, \text{cm} = 0.005 \, \text{m} \)
- Student B: \( LC_B = 0.1 \, \text{cm} = 0.001 \, \text{m} \)
- Student C: \( LC_C = 0.05 \, \text{cm} = 0.0005 \, \text{m} \)

3. **Calculate the Relative Error for Each Student:**
- The formula for relative error is given by:
\[ \text{Relative Error} = \frac{\text{Absolute Error}}{\text{Measured Value}} \times 100\% \]
- The specified length of the room is \( 9.5 \, \text{m} \).

- **For Student A:**
\[ \text{Relative Error}_A = \frac{0.005 \, \text{m}}{9.5 \, \text{m}} \times 100\% \approx 0.0526\% \]

- **For Student B:**
\[ \text{Relative Error}_B = \frac{0.001 \, \text{m}}{9.5 \, \text{m}} \times 100\% \approx 0.0105\% \]

- **For Student C:**
- Since 1 foot = 30.48 cm, the length of the room in feet is:
\[ \text{Length in feet} = \frac{9.5 \, \text{m}}{0.3048 \, \text{m/foot}} \approx 31.17 \, \text{feet} \]
- The number of measurements using the foot scale is approximately 31.
- The absolute error for Student C is:
\[ \text{Absolute Error}_C = 31 \times 0.0005 \, \text{m} = 0.0155 \, \text{m} \]
- Therefore, the relative error for Student C is:
\[ \text{Relative Error}_C = \frac{0.0155 \, \text{m}}{9.5 \, \text{m}} \times 100\% \approx 0.1632\% \]

4. **Compare the Relative Errors:**
- Relative Error for Student A: \( \approx 0.0526\% \)
- Relative Error for Student B: \( \approx 0.0105\% \)
- Relative Error for Student C: \( \approx 0.1632\% \)

5. **Conclusion:**
- Student B reports the lowest relative error in the measured length.

### Final Answer:
**Student B reports the lowest relative error in the measured length.**