A screw gauge and a sphermoeter can measure distances upto

Options

A. `10^(-3)m`
B. `10^(-4)m`
C. `10^(-5)m`
D. `10^(-6)m`

Answer

To determine the maximum measurable distances using a screw gauge and a spherometer, we can follow these steps:

### Step 1: Understand the Instruments
- A **screw gauge** is used to measure small dimensions, such as the diameter of a wire or a small object.
- A **spherometer** is used to measure the radius of curvature of spherical surfaces, such as lenses or mirrors.

### Step 2: Determine the Least Count of Each Instrument
- The **least count** of a screw gauge is typically 0.001 cm, which can also be expressed in meters as:
\[ 0.001 \text{ cm} = 0.001 \times \frac{1}{100} \text{ m} = 10^{-5} \text{ m} \]

- The least count of a spherometer is generally around 0.01 cm, which can be converted to meters as:
\[ 0.01 \text{ cm} = 0.01 \times \frac{1}{100} \text{ m} = 10^{-4} \text{ m} \]

### Step 3: Identify the Maximum Measurement Capability
- The screw gauge can measure distances up to \(10^{-5} \text{ m}\).
- The spherometer can measure distances up to \(10^{-4} \text{ m}\).

### Step 4: Conclusion
- Therefore, the maximum distances that can be measured by a screw gauge and a spherometer are:
- Screw Gauge: \(10^{-5} \text{ m}\)
- Spherometer: \(10^{-4} \text{ m}\)

### Final Answer
The screw gauge can measure distances up to \(10^{-5} \text{ m}\) and the spherometer can measure distances up to \(10^{-4} \text{ m}\).

---