Question

The least count of the meter rod is .1 cm.what is the permissible error in the length of the rod measured with it?

Answer 1

The least count of the meter rod is .1 cm. What is the permissible error in the length of the rod measured with it?

**Solution:**

Use the method of Kornfeld:

$$\Delta x = \frac {x _ {\max} - x _ {\min}}{2}, \Delta x - \text{permissible error}$$ $$x _ {\max} - x _ {\min} = 0.1 \text{ cm}$$

- the minimum difference between two measurements of length permissible error:

$$\Delta x = \frac {x _ {\max} - x _ {\min}}{2} = \frac {0.001 \text{ m}}{2} = 0.0005 \text{ m} (0.05 \text{ cm})$$

Calculate the relative error in measuring meter:

$$\varepsilon = \frac {\Delta x}{1 \text{ m}} * 100\% = \frac {0.0005 \text{ m}}{1 \text{ m}} * 100\% = 0.05\%$$

As we will measure a meter rod, the measurement accuracy is permissible.

**Answer:** 0.05 cm (0.0005 m).