In a vernier callipers, $20$ $VSD$ coincide with $16$ $MSD$ (each division of length $1 \text{ mm}$). The least count of the vernier callipers is: (in $\text{ cm}$)

There are $100$ divisions on the circular scale of a screw gauge of pitch $1 \,mm$. With no measuring quantity in between the jaws,the zero of the circular scale lies $5$ divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that $4$ linear scale divisions are clearly visible while $60$ divisions on the circular scale coincide with the reference line. The diameter of the wire is: (in $\,mm$)

Two full turns of the circular scale of a screw gauge cover a distance of $1 \ mm$ on its main scale. The total number of divisions on the circular scale is $50$. Further,it is found that the screw gauge has a zero error of $-0.03 \ mm$. While measuring the diameter of a thin wire,a student notes the main scale reading of $3 \ mm$ and the number of circular scale divisions in line with the main scale as $35$. The diameter of the wire is ....... $mm$

$A$ steel wire of diameter $0.5 \text{ mm}$ and Young's modulus $2 \times 10^{11} \text{ N m}^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 \text{ m}$. $A$ vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale,of least count $1.0 \text{ mm}$,is attached. The $10$ divisions of the vernier scale correspond to $9$ divisions of the main scale. Initially,the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 \text{ kg}$,the vernier scale division which coincides with a main scale division is. . . . Take $g = 10 \text{ m s}^{-2}$ and $\pi = 3.2$.

Length of $9 \ MSD$ of a vernier caliper are equal to $10 \ VSD$ and $1 \ MSD = 1 \ mm$. For measuring the length of a rod,the reading on the main scale is $6.4 \ cm$ and the $8^{th}$ division on the vernier scale is in line with a marking on the main scale. If there is no zero error,find the length of the rod: (in $cm$)

$A$ spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading : $58.5^{\circ}$
Vernier scale reading : $09$ divisions
Given that $1$ division on the main scale corresponds to $0.5^{\circ}$. The total number of divisions on the Vernier scale is $30$,which matches $29$ divisions of the main scale. The angle of the prism from the above data is ....... . (in $^{\circ}$)