### MEASUREMENT OF LENGTH

MEASUREMENT OF LENGTH

SCREW GAUGE

1. PRINCIPLE OF A SCREW GAUGE

Screw gauge works on the principle of a screw in a nut or micrometer screw.

2. PITCH OF A SCREW

The distance travelled by the tip of the screw for one complete rotation of its head is called the pitch of a screw.

3. LEAST COUNT OF A SCREW GAUGE
Least count of a screw gauge is defined as the ratio of pitch of the screw to the number of head scale divisions(H.S.D.).

4. DESCRIPTION OF A SCREW GAUAGE

F-‘U’shaped metallic frame, S1-stud, S2-tip of the screw , M-milled head

1. A screw gauge consists of U-shaped metallic frame ‘F’ as shown the
figure. To one end of this frame shaft ‘s1’ is fixed.

2. On the opposite end of ‘F’ a hallow long cylinder ‘C’ is fixed.

3. The hallow cylinder has fine threads cut inside it and it serves as a nut.

4. On the outer surface of the hollow cylinder an index line is present which is divided into some equal divisions(0.5mm or 1mm). This serves as the pitch scale ‘P’.

5. A screw with a flat shaft ‘s2’ having threads moves through the cylinder.

6. To the other end of the screw a milled head ‘M’ is connected.

7. To this milled head, one end of the barrel ‘B’ is connected.

8. The other end of this barrel is tapered and has 100 or 50 divisions on it. This is called head scale ‘H’.

9. When the two flat shafts ‘s1’ and ‘s2’ are exactly opposite to each other and are in contact, the distance between them is zero. In this position the edge of the head scale must coincide with the zeroth division of the pitch scale. Further index line must be coinciding with the zero of the head scale.

Determine the diameter of a wire using a screw gauge

1. The least count of a screw gauge is determined first by using the formula.

2. The given wire is placed between the shafts ‘s1’ and ‘s2’ and the head scale is rotated in clock wise direction such that it holds the wire tightly.

3. The value of the pitch scale division which just precedes the edge of the head scale is noted as pitch scale reading (P.S.R).

4. The value of the head scale division which coincides with the index line is observed as head scale reading (H.S.R.).

5. Now the diameter of the wire is determined using the formula.
d=P.S.R + (H.S.R x L.C.)

PRECAUTIONS:-

1. P.S.R. must be taken with out parallax error.

2. Screw must be rotated by holding the milled head provided with the safety device.

3. Same units must be used for P.S.R and least count.

6. POSITIVE ZERO ERROR OF A SCREW GUAGE:-

Index line of pitch scale

If the zeroth division of the head scale is below the index line of the pitch scale the error is said to be Positive and the correction is Negative.
7. NEGATIVE ZERO ERROR OF A SCREW GUAGE:-

Index line of pitch scale

If the zeroth division of the head scale is above the index line of the pitch scale the error is said to be Negative and the correction is Positive.

8. ADVANTAGES OF A SCREW GAUGE:-

Screw gauge is used to measure the thickness of a glass plate, diameter of a wire and the diameter of a small sphere.

Problems:-¬

1. Find the least count of a screw gauge whose head scale is divided into 200 divisions, if it moves 5mm distance when the head is rotated through 5 revolutions.

Given
Least count (l.c.)=?
H.S.D=200
Distance moved(x) =5mm;
Number of revolution (n)=5
We know that

=1mm.

=0.5×10-2
L.C.=0.005mm.

2. While measuring the diameter of a lead shot using a screw gauge the reading on the pitch scale is found to be 7.5mm and that on the head scale is 48. If the least count is 0.01mm and zero error is +0.05mm, find the diameter of the lead shot?

Given,
Least count (L.C)=0.01mm
Zero error=+0.05mm
Zero correction=-0.05mm
d=?
We know that
d=P.S.R. + (C.H.S.RxL.C)
=7.5 + (47.95×0.01)
=7.5 + 0.4795
=7.9795mm
Diameter(d)=7.9795mm

3. The head of a screw gauge is divided into 50 divisions. It advances 1mm when the screw is turned through 2 rotations. Find the pitch of the screw and Least count?

Given
Distance moved(x) = 1mm
No. of rotations (n) = 2
Pitch of the screw (P)=?
L.C. = ?
We know that,

= =0.5mm

=0.01mm
Least Count(L.C.)=0.01mm

4. When the above screw gauge is used to measure the diameter of a nail the P.S.R = 1.5mm and H.S.D=18. Find the diameter of a nail?

Given,
Least count (L.C.)=0.01mm
We know that,
D=P.S.R. + (H.S.R x L.C)
=1.5 + (18×0.01)
=1.5+0.18mm
=1.68mm
The diameter of the nail d=1.68mm

III Match the following:-

A B

1. Least count of the screw gauge (c) a) Micrometer Screw.

2. Principle of the screw gauge (a) b) Screw gauge.

3. Used for finding the thickness of a (b) c)
glass plate

A B

1. Distance between two successive (b) a)P.S.R.+(C.H.S.RxL.C)

2. Diameter of a wire as measured (a) b) Pitch of the screw.
by the screw gauge

IV Fill in the blanks:-

1. The smallest length that can be measured accurately using any scale is called least count.

2. Least count of an ordinary scale is 1mm.

3. Smallest length including the thickness of the glass plate can be measured using a screw gauge upto 0.01mm (or) 0.001 cm (or) fraction of 1mm.

4. A mechanical device used to measure the thickness of a glass piece or a glass plate is a screw gauge.

5. A screw gauge works on the principle of a screw in a nut.
6. Distance between two adjacent threads of a screw is called Pitch of the screw.

7. If the zeroth division of the head scale is below the index line of the pitch scale the error is said to be positive and the correction is negative.

8. If the zeroth division of the head scale is below the index line of the pitch scale the error is said to be negative and the correction is positive.

9. Screw gauge consists of pitch scale and head scale.

10. Pitch of the screw

11. For a screw gauge least count=
L.C. .

12. For measuring the length of any object we must keep our eyes vertically above the divisions.

13. Small lengths that can be measured as diameter of a wire or thickness a wire or a glass plate can be measured to a fraction of 1mm.

14. The distance traveled by the tip of the screw for one full rotation of the head is called pitch of the screw.

15. The divisions marked on the barrel of a screw gauge is called head scale divisions.