A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:

In certain vernier callipers, \(25\) divisions on the vernier scale have the same length as \(24\) divisions on the main scale. One division on the main scale is \(1\) mm long. The least count of the instrument is:

In a vernier calliper, \(N\) divisions of vernier scale coincide with (\(N\text-1\)) divisions of the main scale (in which the length of one division is \(1\) mm). The least count of the instrument should be:
1. \(N~\text{mm}\)
2. \((N-1)~\text{mm}\)
3. \(\frac{1}{10N}~\text{cm}\)
4. \(\frac{1}{(N-1)}~\text{mm}\)

A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: \(0\) mm
Circular scale reading: \(52\) divisions 
Given that \(1\) mm on the main scale corresponds to \(100\) divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:

The pitch of a screw gauge is \(1~\)mm and there are \(100\) divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads \(1\) mm and \(47\)^th division on the circular scale coincides with the reference line. The length of the wire is \(5.6\) cm. Curved surface area (in cm²) of the wire in appropriate number of significant figures will be:

1. \(2.4\) cm²

2. \(2.56\) cm²

3. \(2.6\) cm²

4. \(2.8\) cm²

Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?
It is given that the circular head translates \(P\) MSD in \({N}\) rotations. (\(1\) MSD \(=\) \(1~\text{mm}\).)

              
1. \( \left(\frac{{P}}{{N}}\right)\left(2+\frac{45}{100}\right) \text{mm} \)
2. \( \left(\frac{{N}}{{P}}\right)\left(2+\frac{45}{{N}}\right) \text{mm} \)
3. \(P\left(\frac{2}{{N}}+\frac{45}{100}\right) \text{mm} \)
4. \( \left(2+\frac{45}{100} \times \frac{{P}}{{N}}\right) \text{mm}\)

In an experiment, the height of an object measured by a vernier callipers having least count of \(0.01~\text{cm}\) is found to be \(5.72~\text{cm}\). When no object is there between jaws of this vernier callipers, the reading of the main scale is \(0.1\) cm and the reading of the vernier scale is \(0.3~\text{mm}\). The correct height of the object is:
1. \( 5.72 ~\text{cm} \)
2. \( 5.59~\text{cm} \)
3. \( 5.85~\text{cm} \)
4. \( 5.69~\text{cm} \)

A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument? \(1~\text{msd}= 100~\text{csd}=1~\text{mm}\)