In a vernier callipers,$10$ divisions of vernier scale coincide with $9$ divisions of main scale,the least count of which is $0.1\,cm$. If in the measurement of inner diameter of a cylinder,the zero of the vernier scale lies between $1.3\,cm$ and $1.4\,cm$ of the main scale and the $2^{nd}$ division of the vernier scale coincides with a main scale division,then the diameter will be .......... $cm$.

$A$ student measured the diameter of a wire using a screw gauge with the least count $0.001\, cm$ and listed the measurements. The measured value should be recorded as (in $, cm$)

The diameter of a wire is measured with a screw gauge having a least count of $0.01\;mm$. Which of the following correctly expresses the diameter?

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

The vernier scale used for measurement has a positive zero error of $0.2\, mm$. If while taking a measurement it was noted that the '$0$' on the vernier scale lies between $8.5\, cm$ and $8.6\, cm$ and the vernier coincidence is $6$,then the correct value of measurement is ............. $cm$. (Least count $= 0.01\, cm$)

In an experiment with Vernier callipers of least count $0.1\,mm$,when two jaws are joined together,the zero of the Vernier scale lies to the right of the zero of the main scale and the $6^{th}$ division of the Vernier scale coincides with a main scale division. While measuring the diameter of a spherical bob,the zero of the Vernier scale lies between $3.2\,cm$ and $3.3\,cm$ marks,and the $4^{th}$ division of the Vernier scale coincides with a main scale division. The diameter of the bob is measured as $.......\,cm$.