# Screw Gauge Experiment

**Screw Gauge Experiment for Class 11 ****with Readings**

**Aim:**

i. To determine the diameter of a wire,

ii. To determine the volume of a wire.

iii. To determine the surface area and volume of a lead shot.

iv. To determine the thickness of the glass plate and hence the volume using screw gauge

**Apparatus **

Screw gauge, Wire, Lead shot, Glass plate. Graph paper etc.

Screw gauge consists of a U shaped frame having on one side stud R with plane face and on the other side a hollow cylinder C. A reference line is marked on the cylinder parallel to its axis and it is divided into 1 mm. or ½ mm. This scale is known as pitch scale. Through the hollow cylinder, a tight fitting screw Q works. One end of the screw has a plane face opposite to R. Other end of the screw has a hollow sleeve S with a bevelled edge H which is usually divided into 100 or 50 equal parts and called the head scale. M is milled head or a ratchet.

**Principle **

The least count of the screw gauge is the distance through which the screw advances when it is rotated through one division of the head scale.

i. Least Count (LC) = Pitch/No of divisions on the head scale

Pitch of a screw is the distance through which it advances in one complete rotation of the head scale.

ii. Total Reading = P.S.R. + (corrected H.S.R. x LC)

where,

P.S.R. = Pitch Scale Reading

H.S.R. = Head Scale Reading

L.C. = Least Count

iii. Volume of the wire, V = πr^{2}l

where, r = radius of the wire

l = length of the wire

iv. Surface area of the lead shot

A = 4πa^{2}

v. Volume of the lead shot

V = 4/3 πa^{3}

where, a = radius of the lead shot

vi. Volume of the glass plate V = A x t

where, A = area of the glass plate

t = thickness of the glass plate

**Procedure**

i. To determine pitch and least count of the screw gauge

The pitch is the distance moved by the screw for one complete rotation of the head scale. To find pitch, an even number of complete rotation (say 10) is given to the head of the screw and the distance moved is found on the pitch scale. Dividing this distance by the number of rotations give the pitch.

i.e., Pitch = Distance moved/ Number of rotations

Least count is then found by dividing the pitch by the number of divisions on the head scale.

Least Count (L.C.) = Pitch /No. of divisions on the head scale

The plane faces of stud and tip are made to touch each other. If the zero of the head scale is coinciding with the reference line on the pitch scale, there is no zero correction. If the zero reading on the head scale is below the reference line, the zero correction is negative. If zero reading on the head scale is above the reference line, the zero correction is positive.

ii. To find the diameter of a wire

The given wire is gently pressed between P and Q by working the screw forward. The pitch scale reading (P.S.R.) immediately before the head scale is noted. The head scale reading (H.S.R.) coinciding with the line of the pitch scale is also noted. The zero correction is added to the observed head scale reading to get correct head scale reading. The pitch scale reading is then added to the correct head scale reading which gives the diameter. The experiment is repeated and the mean diameter is noted.

The diameter of the wire (d) = H.S.R. + V.S.R. x L.C.

Half the diameter gives the radius (r). Length of the wire (l) is measured using a scale. Then the volume of the wire is calculated using the formula,

V = πr^{2}l

iii. To find the surface area and volume of lead shot

The diameter (D) and hence radius (a) of the lead shot is found out as explained above. Then the surface area and volume of the lead shot can be calculated using the formulae.

A = 4πa^{2}

V = (4/3)πa^{3}

iv. To find the volume at the glass plate

The thickness (t) of the glass plate is measured as above. Then the glass plate is placed on a graph paper and its outline is traced. The area (A) of the glass plate is found out by counting the squares. Then the volume (V) of the glass plate is calculated using the formula,

V = A x t

**Observations and Calculations**

Distance moved for 5 rotations = __5 mm__

Pitch of the screw = __1 mm__

No of divisions on the head scale = __100__

Least Count = __0.01 mm__

Zero correction = __±10 divisions__

** **

**(a) Volume of the wire**

To find the diameter of the wire

Mean diameter of the wire = __.50 mm__

Mean radius of the wire, r = __0.25 mm__ = __0.25 x 10__^{-3}
m

Length of the wire, l = __7.5 cm__ = __7.5 x 10__^{-2}
m

Volume of the wire, V = πr^{2}l = __1.47 x 10__^{-8}
m^{3}

** **

**(b) Volume of Lead Shot**

Mean diameter of lead shot = __6.21 mm__ = __6.21 x 10__^{-3}
m

Mean radius of lead shot = __3.105 mm__ = __3.105 x 10__^{-3}
m

Volume of lead shot = 4/3 πa^{3} = __125 x 10__^{-9}
m^{3}

** **

**(c) Volume of the glass plate**

To find the thickness of the glass plate

Mean thickness of the glass plate, t = __2.93 mm__ = __2.93
x 10__^{-3} m

Area of the glass plate, A = __794 x 10__^{-2} cm^{2}
= __794 x 10__^{-6} m^{2}

Volume of the glass plate, V = A x t = __2.326 x 10__^{-8}
m^{3}

**Results**

(a) Volume of the wire = __1.47 x
10__^{-8} m^{3}

(b) Volume of lead shot = __125 x
10__^{-9 }m^{3}

(c) Volume of glass plate = __2.326
x 10__^{-8} m^{3}

**MODEL VIVA VOCE QUESTIONS AND ANSWERS**

*1. Another name of screw gauge. *

Micrometer

*2. What is the principle of screw gauge? *

The linear distance moved by screw is directly proportional to the rotation given to the head. This is the principle of the micrometer screw.

*3. Why is screw gauge so named?*

Screw gauge is generally used to measure the diameter of wires which are governed by some standard numbers called standard wire gauge. As the screw gauge makes use of a screw for such measurements, it is named screw gauge.

*4. What is zero error of the screw gauge?*

When the screw tip is in contact with the stud and the zero line of the head scale does not coincide with the reference line of the pitch scale, there is zero error.

*5. What is the basic function of a ratchet?*

It prevents the screw being pressed too hard or too son against the object

*6. Define pitch of the screw gauge *

The pitch of the %mu gauge is the distance moved by the screw for one complete rotation of the head scale.

Pitch = Distance moved /Number of rotations

*7. A screw gauge has 100 divisions on its head scale and the
pitch of the screw is 1 mm. What is its least count? *

Least count = 1mm/100 = 0.01mm

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