The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

Two students, A and B, measure the length of a table. Student A reports the length as $2.350 \pm 0.001$ m, and student B reports it as $2.35 \pm 0.01$ m.  Which student's measurement is more precise, and what is the relative uncertainty in the more precise measurement?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Precision and Uncertainty
	**Related Topics**: Measurement, Error Analysis, Significant Figures
	**Prerequisites**: Understanding of uncertainty and its representation.
## SOLUTION PATHWAY
**Given Information**:
	Student A: $2.350 \pm 0.001$ m
	Student B: $2.35 \pm 0.01$ m
**Method & Steps**:
	1. **Compare Uncertainties:**
		Reasoning: The smaller the uncertainty, the more precise the measurement.
		Student A's uncertainty: $0.001$ m
		Student B's uncertainty: $0.01$ m
	2. **Identify More Precise Measurement:**
		Working: Since $0.001$ m < $0.01$ m, Student A's measurement is more precise.
		Key Point: Precision relates to the spread of measurements.
	3. **Calculate Relative Uncertainty:**
		Result: Relative uncertainty = (Absolute uncertainty) / (Measured value)
		For Student A: $0.001$ m / $2.350$ m = $0.0004255... \approx 0.00043$
		Verification: The relative uncertainty is dimensionless and often expressed as a percentage.
## OPTION ANALYSIS
[A] ✓: Student A's measurement is more precise because the uncertainty is smaller ($0.001$ m vs. $0.01$ m). The relative uncertainty for Student A is $0.001/2.350 = 0.00043$.
[B] :x: Student B's measurement has a larger uncertainty, making it less precise. The relative uncertainty calculation is also incorrect.
[C] :x: While correctly identifying Student A as more precise, the relative uncertainty is calculated for Student B.
[D] :x: Incorrectly identifies Student B as more precise and uses the incorrect relative uncertainty.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing precision with accuracy: Precision refers to the consistency of measurements, while accuracy refers to how close a measurement is to the true value.
		2. Incorrectly calculating relative uncertainty: Remember to divide the absolute uncertainty by the measured value.
	**Quick Tips**:
		1. Smaller uncertainty = Higher precision.
		2. Relative uncertainty is a useful way to compare the precision of different measurements.

Mr. ANIL KUMAR.G · Answer

The correct Option is "Student A's measurement is more precise, and the relative uncertainty is 0.00043."

Mr. ANIL KUMAR.G · Answer

Student B's measurement is more precise, and the relative uncertainty is 0.0043.

Mr. ANIL KUMAR.G · Answer

Student A's measurement is more precise, and the relative uncertainty is 0.0043.

Mr. ANIL KUMAR.G · Answer

Student B's measurement is more precise, and the relative uncertainty is 0.00043.

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