Question

(i) Answer the following:
You are given a thread and a metre scale. How will you estimate the diameter of the thread?

(ii)Answer the following:
A screw gauge has a pitch of $1.0mm$ 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?

(iii) Answer the following:

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?

Answer 1

(i)Given: Thread and metre scale
The diameter of a thread is so small that it cannot be measured using a meter scale. We wind a number of turns of the thread on the meter scale so that the turns are closely touching one another. Measure the length $\left(Z\right)$ of the windings on the scale which contains n number of turns
Diameter of thread $\left(d\right)=\frac{Z}{n}$

(ii)Given: Instrument- Screw gauge

$LC=\frac{\text{pitch}}{\text{no of divisions on circular scales}}$

$\therefore$ theoretically speaking, least count decreases on increasing the number of divisions on the circular scale. Hence, accuracy would increase. Practically, it may not be possible to take the reading precisely due to low resolution of human eye.

(iii) A large number of observations (say, $100$) will give more reliable result than smaller number of observations (say, $5$).

This is because larger the number of readings, closer is the arithmetic mean to the true value and hence smaller the random error.