Units and Measurements

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

1. 0.07 cm negative zero error
2. 0.7 cm negative zero error
3. 0.07 cm positive zero error
4. 0.7 cm positive zero error

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.

1. 1 10-2
2. 1 10-3
3. 5 10-2
4. 5 10-3

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.

1. 5.045
2. 5.055
3. 5.450
4. 5.550

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4th mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5th division of vernier scale coincides with a main scale division. Measured length of cylinder is mm. (Least count of Vernier calliper = 0.1 mm)

1. 15.5
2. 15.4
3. 15.9
4. 15.1

In an experiment, a set of readings are obtained as follows: 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is mm.

1. 0.01
2. 0.05
3. 0.001
4. 0.1

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is mm.

1. 0.002
2. 0.02
3. 0.05
4. 0.005

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is mm. [Assume least count is 0.01 mm]

1. 1.54
2. 1.50
3. 1.51
4. 1.48

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be x100 where x is .

The least count of a screw gauge is 0.01 mm. If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50%, the new least count will be 10-3 mm.

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below.

1. Both Statement I and Statement II are false
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are true
4. Statement I is false but Statement II is true

One main scale division of a vernier caliper is equal to m units. If nth division of main scale coincides with (n + 1)th division of vernier scale, the least count of the vernier caliper is :

1. 1(n + 1)
2. m(n + 1)
3. n(n + 1)
4. mn(n + 1)

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm. The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is:

1. 2.2 g/cm3
2. 2.0 g/cm3
3. 1.7 g/cm3
4. 2.5 g/cm3

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 circular scale coincide with the reference line. The diameter of the wire is :

1. 4.65 mm
2. 4.60 mm
3. 4.55 mm
4. 3.35 mm

Least count of a vernier caliper is 120 N cm. The value of one division on the main scale is 1 mm. Then the number of divisions of main scale that coincide with N divisions of vernier scale is :

1. ( 2N - 12N )
2. ( 2N - 120N )
3. (2N - 1)
4. ( 2N - 12 )

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is x50 mm. The value of x is :

1. 42
2. 71
3. 21
4. 142

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?

1. 5
2. 40
3. 10
4. 20

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to mm.

1. 5
2. 2
3. 1
4. 0.5

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

1. 511
2. 1011
3. 5011
4. 12

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of traveling microscope is

1. 0.01 mm
2. 0.01 cm
3. 0.1 mm
4. 0.1 cm

Identify the physical quantity that cannot be measured using spherometer :

1. Radius of curvature of concave surface
2. Specific rotation of liquids
3. Thickness of thin plates
4. Radius of curvature of convex surface

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

1. Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true