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 $50$. 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 $35^{\text{th}}$ division of the circular scale coincides with the reference line of the main scale. The diameter of the wire is: (in $mm$)

While measuring the diameter of a wire using a screw gauge, the following readings were noted. The main scale reading is $1 \,mm$ and the circular scale reading is equal to $42$ divisions. The pitch of the screw gauge is $1 \,mm$ and it has $100$ divisions on the circular scale. The diameter of the wire is $\frac{x}{50} \,mm$. The value of $x$ is:

$A$ 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 $\pi = 3.2$.

The one division of main scale of vernier callipers reads $1\,mm$ and $10$ divisions of Vernier scale is equal to the $9$ divisions on main scale. When the two jaws of the instrument touch each other the $zero$ of the Vernier lies to the right of $zero$ of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws,the $zero$ of the Vernier scale lies in between $4.1\,cm$ and $4.2\,cm$ and $6^{\text{th}}$ Vernier division coincides with a main scale division. The diameter of the bob will be $.............10^{-2}\,cm$

$A$ screw gauge has a least count of $0.01\, mm$ and there are $50$ divisions on its circular scale. The pitch of the screw gauge is $........\, mm$.

Student $A$ and Student $B$ used two screw gauges of equal pitch and $100$ equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322 \, \text{cm}$. The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is .... .
Given pitch $= 0.1 \, \text{cm}$.