Least count

Two thin wires, Wire-1 of diameter $0.650$ mm and Wire-2 of unknown diameter $d$ are given. To obtain the value of $d$, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of $0.5$ mm and there are $100$ divisions on the circular scale (CS). The smallest division on the linear scale (LS) is $0.5$ mm. The table shows the readings of LS and CS for the measurements. The value of $d$ (in µm) is:

	LS (mm)	CS
Wire-1	0.5	42
Wire-2	1.5	95

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is ________ mm.

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

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7th Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $D$ of a tube. The measured value of $D$ is:

The dimensions of a cone are measured using a scale with a least count of $2\,\mathrm{mm}$. The diameter of the base and the height are both measured to be $20.0\,\mathrm{cm}$. The maximum percentage error in the determination of the volume is _____.

In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier contant will be ______ $\times10^{-2}$ mm.

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ $\times10^{-6}$ m.

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4$^{\text{th}}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6$^{\text{th}}$ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :

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 ______ $\times10^{-2}$ cm.

A travelling microscope has 20 divisions per cm on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers $(C_1)$ has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper $(C_2)$ has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers $C_1$ and $C_2$, respectively, are

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:

During Searle's experiment, zero of the Vernier scale lies between $3.20\times10^{-2}$ m and $3.25\times10^{-2}$ m of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between $3.20\times10^{-2}$ m and $3.25\times10^{-2}$ m of the main scale but now the 45th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is $8\times10^{-7}\ \mathrm m^2$. The least count of the Vernier scale is $1.0\times10^{-5}$ m. The maximum percentage error in the Young's modulus of the wire is

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it ?