In an experiment,the angles are required to be measured using an instrument where $29$ divisions of the main scale exactly coincide with $30$ divisions of the vernier scale. If the smallest division of the main scale is half a degree $(= 0.5^\circ)$,then the least count of the instrument is:

The circular scale of a micrometer has $200$ divisions and a pitch of $2 \, mm$. Find the measured value of the thickness of a thin sheet in $mm$.

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?

In a vernier callipers,each $cm$ on the main scale is divided into $20$ equal parts. If the $10^{th}$ vernier scale division coincides with the $9^{th}$ main scale division,then the value of the vernier constant will be $\dots \; \times 10^{-2} \; mm$.

In a screw gauge,$5$ complete rotations of the screw cause it to move a linear distance of $0.25\, cm$. There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error,the thickness of the wire is (in $, cm$)

If $50$ Vernier divisions are equal to $49$ main scale divisions of a travelling microscope and one smallest reading of main scale is $0.5 \,mm$, the Vernier constant of travelling microscope is: