Question

Answer the following:
(a) We are having a thread and a metre scale. How can the diameter of the thread be estimated?
(b) A screw gauge is having a pitch of $1.0mm$ and $200$ divisions on the circular scale. Do you think it is possible to enhance the accuracy of the screw gauge randomly by enhancing the number of divisions on the circular scale?
(c) The mean diameter of a thin brass rod is to be determined using Vernier callipers. Why a set of $100$ measurements of the diameter expected to gain a more reliable estimate than a set of $5$ measurements only?

Answer 1

Hint: A screw gauge is an instrument used in the physics experiments in order to measure the smaller diameters and the lengths of the wires or equipment. It is sometimes referred to as a micrometer. Diameters can be found by taking the ratio of the length of the rod to the number of turns. This all will help you in answering this question.

Complete step by step answer:
(a) Wrap a thread on a uniform smooth rod in a way that the coils therefore created are very close to each other. Using a meter scale, measure the length of the thread. The diameter of the thread is found by the equation given as,
$\text{diameter = }\dfrac{\text{length of rod}}{\text{number of turns}}$
(b) The enhancement of the accuracy of a screw gauge by enhancing the number of divisions of the circular scale is not possible. When the number of divisions of the circular scale is made higher, its accuracy also enhances to a particular extent only.
(c) A set of $100$ measurements is more reliable than a set of $5$ measurements. This is due to the random errors involved in the first case being very small when compared to the second one.

Note: A screw gauge is working based on the principle of the screw. We get the linear movement of the main scale by the rotation of the screw head. This linear movement is helpful in determining the thickness of the metal plate or the diameter of wire.