# (solved)Questions 2.7, 2.8 of NCERT Class XI Physics Chapter 2

The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only? . . . and 2 more questions

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### Question 2.7 NCERT Class XI Physics

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair ?

### Solution

The (avg) thickness at $\displaystyle 100 \text{X} = 3.5 \text{ mm}$

$\displaystyle \therefore \text{thickness} = \frac{3.5}{100} = 0.035 \text{ mm} \:\underline{Ans}$

### Question 2.8(b) NCERT Class XI Physics

A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale ?

### Solution

First reason is that a human eye cannot differentiate between very fine divisions.

Second is that manufacturing of such a screw gauge would be costly.

### Question 2.8(c) NCERT Class XI Physics

The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only ?

### Solution

The thickness is so small that personal and random errors can affect the accuracy.

Therefore, the arithmetic mean of 100 observations would be very close to the true value of the diameter of the rod.