In a screw gauge,$5$ complete rotations of the circular scale give a $1.5 \, mm$ reading on the linear scale. The circular scale has $50$ divisions. The least count of the screw gauge is: (in $, mm$)

$A$ vernier callipers used by a student has $20$ divisions in $1\;cm$ on the main scale. $10$ vernier divisions coincide with $9$ main scale divisions. When the jaws are closed,the zero of the main scale is to the left of the zero of the vernier scale,and the $6^{th}$ division of the vernier scale coincides with a main scale division. The student places a wooden cylinder between the jaws to measure its length. The zero of the vernier scale is to the right of the $3.20\;cm$ mark,and the $8^{th}$ vernier division coincides with a main scale division. When measuring the thickness (diameter) of the cylinder,the zero of the vernier scale lies to the right of the $1.50\;cm$ mark,and the $6^{th}$ vernier division coincides with a main scale division. The correct values of the measured length and diameter are respectively:

In a screw gauge,when the circular scale is given five complete rotations,it moves linearly by $2.5 \text{ mm}$. If the circular scale has $100$ divisions,the least count of the screw gauge is . . . . . . $\text{mm}$.

The circular divisions of a screw gauge are $50$. It moves $0.5 \ mm$ on the main scale in one rotation. When the diameter of a wire is measured,the main scale reading is $3.5 \ mm$ and the circular scale reading is $32$. If the zero error (positive) in the screw gauge is $0.06 \ mm$,then the diameter of the wire is:

$A$ screw gauge with a pitch of $0.5 \ mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement,it is found that when the two jaws of the screw gauge are brought in contact,the $45^{th}$ division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in $mm$) if the main scale reading is $0.5 \ mm$ and the $25^{th}$ division coincides with the main scale line?

The least count of the main scale of a vernier callipers is $1\, mm$. Its vernier scale is divided into $10$ divisions and coincides with $9$ divisions of the main scale. When jaws are touching each other,the $7^{th}$ division of the vernier scale coincides with a division of the main scale and the zero of the vernier scale lies to the right side of the zero of the main scale. When this vernier is used to measure the length of a cylinder,the zero of the vernier scale is between $3.1\, cm$ and $3.2\, cm$ and the $4^{th}$ $VSD$ coincides with a main scale division. The length of the cylinder is $.....\, cm$. ($VSD$ is vernier scale division)