3. Measure the internal diameter and depth of a given beaker using Vernier calipers and hence find it’s Volume.

Aim:- To measure internal diameter and depth of a given beaker using Vernier calipers and hence find it’s Volume.

Apparatus:- Vernier calipers, a beaker and a magnifying glass.

Theory:-

For measuring internal diameter and depth:

     If with the body between the jaws, the zero of Vernier scale lies ahead of N^th division of main scale, then main scale reading (M.S.R.) = N.

     If nth division of Vernier scale coincides with any division of main scale,

then Vernier scale reading (V.S.R) = n x (L.C.) (L.C. is least count of Vernier callipers)

                                                       = n x (V.C.) (V.C. is Vernier constant of Vernier callipers)

Total reading, T.R = M.S.R + V.S.R (L.C. = V.C.)

                              =N+ n x (V.C)

For Volume:

Volume of beaker = internal area of cross section x depth

            Or             V = π(D/2)².d

Where, D = Internal diameter of beaker

               d = Depth of beaker

Observation:-

Known mass of the block (m) = ……. g.

Determination of Vernier Constant (Least Count) of the Vernier Callipers

                    1 M.S.D = 1mm

                    1O V.S.D = 9 M.S.D

Therefore, 1 V.S.D = M.S.D = 0.9 mm.

Vernier Constant, V.C = 1 M.S.D - 1 V.S.D = (1 — 0.9) mm = 0.1 mm = 0.01 cm.

Zero error (i) ...... cm, (ii)..... cm, (iii) ...... cm.

Mean zero error (e) = ...... cm.

Mean zero correction (c) = - e = ...... cm.

Table for the Internal Diameter (D):-

Serial Number	Main Scale Reading	Vernier Scale Reading		Total Reading
		No. of Vernier division coinciding(n)	Value [n x (V.C)]	Observed  [Do = N + n x (V.C)]	Corrected (D = Do + C)
1					D1
2					D2
3					D3
4					D4
5					D5
6					D6

Internal diameter of beaker

Table for the Depth (d):-

Serial Number	Main Scale Reading	Vernier Scale Reading		Total Reading
		No. of Vernier division coinciding(n)	Value [n x (V.C)]	Observed  [do = N + n x (V.C)]	Corrected (d = do + C)
1					d1
2					d2
3					d3
4					d4
5					d5
6					d6

 

Depth of beaker

Calculations:-

Mean corrected internal diameter: D = D₁ + D₂ + D₃ + D₄ + ­D₅ + ­D₆ / 6

Mean corrected depth: d = d₁ + d₂ + d₃ + d₄ + ­d₅ + ­d₆ / 6

Volume of the beaker = π(D/2)².d

Result:-

The volume of the beaker is ……… cm³.

Precautions:-

1. Motion of Vernier scale on main scale should be made smooth (by oiling if necessary).
2. Vernier constant and zero error should be carefully found and properly recorded.
3. The body should be gripped between the jaws firmly but gently (without undue pressure on it from the jaws).
4. Observations should be taken at right angles at one place and taken at least as three different places.

Sources of Error:-

1. The Vernier scale may be loose on main scale.
2. The jaws may not be at right angles to the main scale.
3. The graduations on scale may not be correct and clear.