2. Measure the dimensions of a given regular body of known mass using Vernier callipers and hence find it’s density.

Aim:- To measure the dimensions of a given regular body of known mass using Vernier callipers and hence find it’s density.

Apparatus:- Vernier callipers, a spherical body (pendulum bob) or a cylinder and a magnifying lens.

Theory:-

For measuring dimensions:

      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 rectangular block = Length x Breadth x Thickness(height).

Density = Mass / Volume

i.e p = m/v

Vernier callipers - Measuring dimensions of a rectangular metallic block.

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 Length:-

Serial Number	Main Scale Reading	Vernier Scale Reading		Total Reading
		No. of Vernier division coinciding	Value[n x (V.C)]	Observed  Lo = N + n x (V.C)	Corrected L = Lo + C
1					L1
2					L2
3					L3
4					L4
5					L5
6					L6

Table for the breadth:-

Serial Number	Main Scale Reading	Vernier Scale Reading		Total Reading
		No. of Vernier division coinciding	Value [n x (V.C)]	Observed  Bo= N + n x (V.C)	Corrected B = Bo + C
1					B1
2					B2
3					B3
4					B4
5					B5
6					B6

Table for the Height:-

Serial Number	Main Scale Reading	Vernier Scale Reading		Total Reading
		No. of Vernier division coinciding	Value [n x (V.C)]	Observed Ho= N + n x (V.C)	Corrected H = Ho + C
1					H1
2					H2
3					H3
4					H4
5					H5
6					H6

Calculations:-

Mean corrected length of the block, 
L = L₁ + L₂ + L₃ + L₄ + ­L₅ + ­L₆ / 6 = L_m

Mean corrected breadth of the block, 
B = B₁ + B₂ + B₃ + B₄ + B₅ + B₆ / 6 = B_m

Mean corrected height of the block, 
H = H₁ + H₂ + H₃ + H₄ + H₅ + H₆ / 6 = H_m

Volume of the block, V = L_m x B_m x H_m

Density of the block, p = m/v

Result:-

Density of the block material = …….. g/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.
4. Parallax may be there in taking observations.