Let's break down and answer each part of the question step-by-step.
### 1. Smallest Quantity Comparison
We need to compare the following weights to determine the smallest quantity:
- (a) 0.01 g
- (b) 2 mg = 0.002 g
- (c) 100 μg = 0.0001 g
- (d) 5000 mg = 5 g
When we convert each unit to grams, we can compare them directly:
- [tex]\( 0.01 \, \text{g} \)[/tex]
- [tex]\( 2 \, \text{mg} = 0.002 \, \text{g} \)[/tex]
- [tex]\( 100 \, \mu\text{g} = 100 \times 10^{-6} \, \text{g} = 0.0001 \, \text{g} \)[/tex]
- [tex]\( 5000 \, \text{mg} = 5000 \times 10^{-3} \, \text{g} = 5 \, \text{g} \)[/tex]
Clearly, [tex]\( 100 \, \mu\text{g} \)[/tex] or [tex]\( 0.0001 \, \text{g} \)[/tex] is the smallest quantity among these options.
### 2. Suitable Instrument for Measuring the Internal Diameter of a Test Tube
The tools given for measuring the internal diameter of a test tube are:
- (a) meter rule
- (b) vernier calipers
- (c) measuring tape
- (d) screw gauge
Among these instruments, the most suitable tool for measuring the internal diameter of a test tube is:
- (b) vernier calipers
Vernier calipers are designed to measure both external and internal dimensions accurately, typically up to a precision of 0.01 cm or 0.1 mm, making them well-suited for this task.
### 3. Student's Claimed Measurement
The student claimed the diameter of the wire as 1.032 cm using vernier calipers.
When using vernier calipers, measurements are typically read to the nearest hundredth of a centimeter (0.01 cm). Therefore, a measurement of 1.032 cm is plausible since vernier calipers can indeed measure to this level of precision.
### Summary
1. Smallest quantity among the given weights:
- [tex]\( 100 \, \mu\text{g} = 0.0001 \, \text{g} \)[/tex]
2. Most suitable instrument for measuring the internal diameter of a test tube:
- Vernier calipers
3. Student’s measured value with vernier calipers:
- 1.032 cm is a reasonable measurement for diameter, as vernier calipers can measure with such precision.
The results are consistent with the calculations and provide a clear answer to each part of the problem.
