To Measure The Diameter Of Small Spherical Cylindrical Body Using Vernier Callipers - Practice Questions & MCQ

A Vernier caliper is an instrument that measures internal or external dimensions and distances. It allows you to take more precise measurements than you could with regular rulers. 

Important terminologies -

LEAST COUNT AND ZERO ERROR

The magnitude of the smallest measurement that can be measured by an instrument accurately is called its least count (L.C.).

The difference between one main scale division (M.S.D.) and one vernier scale division is called least count.

                                                  i.e.  L.C. = One M.S.D. – One V.S.D.

ZERO ERROR

If there is no object between the jaws (i.e., jaws are in contact), the vernier should give zero reading. But due to some extra material on jaws, even if there is no object between the jaws, it gives some excess reading. This excess reading is called zero error.

Zero correction : Zero correction is invert of zero error.

Zero correction = – (Zero error)

Actual reading = observed reading – excess reading (zero error)
                        = observed reading + zero correction

Aim of the experiment

To measure diameter of a small sphericallcylindrical body using Vernier Callipers.

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

Theory

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

If with division of vernier scale coincides with any division of main scale, then vernier scale reading (V.S.R.)

= n × (L.C.)                                                  ( Here, L.C. is least count of vernier callipers)

= n × (V.C.)                                                  ( Here, V.C. is vernier constant of vernier callipers)

And total reading, T.R. = M.S.R. + V.S.R. = N + n × (V.C.)

Procedure

1. Determine the vernier constant (V.C.) i.e. least count (L.C.) of the vernier callipers and record it stepwise.
2. Bring the movable jaw BD in close contact with the fixed jaw AC and find the zero error. Do it three times and record them. If there is no zero error, record zero error nil.
3. Open the jaws, place the sphere or cylinder between the two jaws A and B and adjust the jaw DB, such that it gently grips the body without any undue pressure on it. Tight the screw S attached to the vernier scale V.

4. Note the position of the zero mark of the vernier scale on the main scale. Record the main scale reading just before the zero mark of the vernier scale. This reading ( 1 ST) is called main scale reading (M.S.R.).
(Mote the number ( n ) of the vernier scale division which coincides with some division of the main scale.
6. Repeat steps 4 and 5 after rotating the body by  for measuring the diameter in a perpendicular direction.

7. Repeat steps 3,4,5 and 6 for three different positions. Record the observations in each set in a tabular form.
8. Find total reading and apply zero correction.
9. Take mean of different values of diameter and show that in the result with proper unit.

Observations: 

1. Vernier constant (least count) of the Vernier Callipers:

$
1 \mathrm{M} . \mathrm{S} . \mathrm{D} .=1 \mathrm{~mm}
$

10 vernier scale divisions $=9$ main scale divisions
i.e. $\quad 10$ V.S.D. $=9$ M.S.D.

$
\therefore \quad \text { 1 V.S.D. }=\frac{9}{10} \text { M.S.D. }
$

Vernier Constant $(\mathrm{V} . \mathrm{C})=1$ M.S.D. - 1 V.S.D. $=1$ M.S.D. $-\frac{9}{10}$ M.S.D.

$
\begin{aligned}
& =\left(1-\frac{9}{10}\right) M . S . D .=\frac{1}{10} \times 1 M . S . D . \\
& =\frac{1}{10} \times 1 \mathrm{~mm}=0.1 \mathrm{~mm}=0.01 \mathrm{~cm}
\end{aligned}
$

2. Zero error: (i) cm (ii) $\qquad$ cm (iii) $\qquad$ .cm

Mean Zero Error (e) = $\qquad$ cm

Mean Zero Correction $(\mathrm{c})=-($ Mean Zero Error $)$
$=$ cm

PRECAUTIONS

• Make the motion of vernier scale on main scale very smooth (by oiling).

• Find the vernier constant and zero error carefully and record them properly.

• Grip the body between the jaws formerly but gently.

• Take atleast observation at three different places at right angles at each place.

• No parallax should be there.