Vernier Caliper

Q. In a vernier calipers , one main scale division is $x\text{cm}$ and $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of main scale. The least count (in $\text{cm}$) of the caliper is:

1. $\left(\frac{n-1}{n}\right)$
2. $\frac{nx}{(n-1)}$
3. $\frac{x}{n}$
4. $\frac{x}{x-1}$

Q. In a vernier caliper, 10 vernier scale divisions are equal to 9 main scale divisions. One main scale division is 1 mm. The device has some zero error as shown in the figure (a). When a cylinder of diameter D is inserted between them, the reading of scale is shown in figure (b). Then, the diameter of the cylinder in cm is

Q. A vernier callipers has its main scale of 10cm equally divided into 200 parts. Its vernier scale of 25 divisions coincide , with 12mm on main scale. The least count is

Q. In a vernier calipers $10$ smallest divisions of the vernier scale are equal to $9$ smallest divisions of the main scale. If the smallest division of the main scale is half millimeter, then the vernier constant is:

1. $0.005\text{mm}$
2. $0.05\text{mm}$
3. $0.5\text{mm}$
4. $0.01\text{mm}$

Q. In a Vernier callipers, N division of Vernier co-inside with (N-1) divisions of main scale in which the length of 1 division is 1 mm. The least count of the instrument in cm is,

1. N
2. $\frac{1}{N}-1$
3. $N-1$
4. $\frac{1}{10N}$

Q. In a vernier calipers having 10 VSD, the vernier constant is 0.1 mm. When the jaws are closed, zero of vernier lies to the left of zero of mainand $7^{th}$ Vsd coincides with a main scale division. When a cylinder is placed between the jaws the main scale reading was 7.7 cm and vernier scale read 8 divisions. What is the diameter of the cylinder ?

1. 77.5 mm
2. 77.8 mm
3. 78.5 mm
4. 78.1 mm

Q. The main scale of vernier calipers reads in millimeter, and its one main scale division is equal to one millimeter. Its vernier is divided into $6$ divisions, which coincide with $15$ divisions of main scale. Furthermore, when a cylinder is tightly placed along its length between two jaws, it is observed that the zero vernier scale lies just right to the $25$th division of the main scale and the fifth division of the vernier scale coincide with $38$th division of the main scale. The measured value is $\frac{2550}{n}$ millimeter.

Q.
It is given that 5 main scale division of a vernier caliper coincide with 6 vernier scale divisions. When jaws are closed zeros of both scale do not coincide and has a negative zero error. Find magnitude of this zero error in mm. 1 main scale division is equal to 1mm.

Q.

Least count/hop count of main scale of a vernier callipers is defined as:

Q.

The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions if each main scale division is 0.5 mm. Calculate the minimum inaccuracy in the measurement of distance.

Q. Let $A$ represents the least count of a vernier caliper whose 10 main scale divisions are equal in length to 12 vernier scale divisions, and one main scale division is equal to 1 mm. Say $B$ represents the least count of a screw gauge with 25 circular scale divisions and a pitch of 1 mm, $A-B$ in mm is

Q. The smallest division on the main scale of a Vernier callipers is $1\text{mm}$ and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a ring, the zero mark of the vernier scale lies between $5.0\text{cm}$ and $5.1\text{cm}$ and the eighth division of the vernier scale coincides with a main scale division. The diameter of the ring is :

1. $5.06\text{cm}$
2. $5.08\text{cm}$
3. $5.04\text{cm}$
4. $5.02\text{cm}$

Q. In a vernier calliper, one main scale division is $xcm$ and $n$ divisions of the vernier scale coincide with $(n-1)$ division of the main scale. The least count (in cm) of the callipers is.

1. $\frac{nx}{n-1}$
2. $\left(\frac{n-1}{n}\right)x$
3. $\frac{x}{n-1}$
4. $\frac{x}{n}$

Q. The length of a rectangular plate is measured by a meter scale and is found to be $10.0\text{cm}$ . Its width is measured by vernier callipers as $1.00\text{cm}$ . The least count of the meter scale and vernier callipers are $0.1\text{cm}\text{and}0.01\text{cm}$ respectively. Maximum permissible error in area measurement is

1. Zero
2. $\pm 0.1{\text{cm}}^2$
3. $\pm 0.3{\text{cm}}^2$
4. $\pm 0.2{\text{cm}}^2$

Q. The vernier of a circular scale is divided into 50 divisions which coincides with 49 main scale division .Each main scale division is 0.5${}^o$.The least count of the instrument is

1. 1'
2. 6'
3. 30'
4. 0.6'

Q. A vernier callipers has its main scale graduated in mm and 10 divisions on its vernier scale are equal in length to 9 mm. When the two jaws are in contact. the zero of vernier scale is ahead of zero of main scale and 3rd division of vernier scale coincides with a main scale division. The zero error of the vernier callipers is $3\times {10}^{-x}cm$. Find the value of x.

Q. Q. A Vernier callipers has its main scale of 1 cm equally divided into 10 equal parts. 20 vernier scale divisions is equal to 19 main scale divisions. Using this vernier a student measures the diameter of wire. He found that main scale reads 2 small divisions and 4th division of vernier scale coincide with a main scale division. The diameter of the wire is (a) 2.02 mm (b) 2. 2 mm (c) 2.5 mm (d) 2.1 mm

Q. A Vernier callipers has $1$ mm marks on the main scale. It has $20$ equal divisions on the Vernier scale which match with $16$ main scale divisions. For this Vernier callipers, the least count is?

1. $0.05$ mm
2. $0.02$ mm
3. $0.1$ mm
4. $0.2$ mm

Q. In a hypothetical vernier calipers $10$ equal divisions on the vernier scale coincide with $6$ main scale divisions. If one division of main scale is $0.5mm$ then the least count is

1. $0.1mm$
2. $0.02mm$
3. $0.3mm$
4. $0.4mm$

Q. In a Vernier callipers having 10 VSD, the Vernier constant is 0.1 mm. When the jaws are closed, zero of Vernier lies to the left of zero of main and 7th VSD coincides with a main scale division. When a cylinder is placed between the jaws of main scale reading was 7.7 cm and Vernier scale read 8 divisions. On the bases of above information answer the following question.

2. A

Q. When a screw gauge with a least count of 0.01 mm is used to measure the diameter of a wire, the reading on the sleeve is found to be 1 mm and the reading on the thimble is found to be 27 divisions.
(i) What is the diameter of the wire in $cm$?
(ii) If the zero error is +0.005 cm, what is the correct diameter?

Q. A vernier callipers has 20 divisions on the vernier scale which coincide with 19 divisions on the main scale .The least count of the instrument is 0.1mm. The main scale division are of (A) 0.5mm. (B) 1mm (C) 2mm. (D)1/4mm

Q. L.C. of vernier calipers is

1. 1 MSD $\times$ Number of VSD's
2. both (a) and (b)
3. 1 MSD $÷$ Number of VSD's
4. 1 MSD - Number of VSD's

Q. The vernier scale of a travelling microscope has $50$ divisions which coincide with 49 main scale divisions. If each main scale division is $0.5$ mm, then the least count of the microscope is

1. $0.01cm$
2. $0.5mm$
3. $0.5cm$
4. $0.01mm$

Q. The length of a uniform rod is 100.0 cm and radius is 1.00 cm. If length is measured with a meter rod having least count 1mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder is

Q. A faulty thermometer has its fixed points marked at $5^{o}C$ and ${95}^{o}C$. This thermometer reads the temperature of a body as ${59}^{o}C$. The correct value is:

1. ${59}^{o}C$
2. ${28.89}^{o}C$
3. ${8.6}^{o}C$
4. ${60}^{o}C$

Q. Consider the following data for a vernier calliper:
10 main scale division = 1 cm.
10 vernier division matches with 9 Main scale division.

While measuring the zero error of the vernier we see that zero of vernier scale is to the right of the zero marking of the main scale with $6^{th}$ vernier division coinciding with main scale divisions.

The actual reading for length measurement is 4.3 cm with 2nd vernier division coinciding with main scale graduation.

Estimate the length.

1. 4.32 $cm$

2. 4.38 $cm$

3. 4.26 $cm$

4. 4.36 $cm$

Q. A 0.5 kg ball is dropped from the height of 10 m above the sidewalk. Calculate the speed of the ball just before it strikes the sidewalk?

1. 200 m/s
2. 10 m/s
3. 14 m/s
4. 28 m/s
5. 5 m/s

Q. The vernier scale of a callipers has 50 divisions which coincide with 49 main scale divisions. If each main scale division is of 0.5mm, then the minimum inaccuracy in the measurement by callipers is (1.) 0.02 cm (2.) 0.02 mm (3.) 0.01 mm (4.) 0.01 cm

Q. The diameter of a cylinder is measured using a Vernier calipers with no zero error. It is found that the zero of the Vernier scale lies between $5.10\text{cm}$ and $5.15\text{cm}$ of the main scale. The Vernier scale has $50$ divisions equivalent to $2.45\text{cm}$. The ${24}^{th}$ division of the Vernier scale excatly coincides with one of the main scale divisions. The diameter of the cylinder is :-

1. $5.112\text{cm}$
2. $5.124\text{cm}$
3. $5.136\text{cm}$
4. $5.148\text{cm}$