Page 12 - Physics - XI

or n V.S.D. = (n – 1) M.S.D.

1 V.S.D. = (n − 1) M.S.D.
n
By the defi nition of Vernier constant, we have Vernier constant (V.C.) = 1 M.S.D. – 1 V.S.D.

(n − 1)
V.C. = 1 M.S.D. – M.S.D.
n
n 1
V.C. = 1 M.S.D.

n
1
V.C. = M.S.D.
n

Valueofthe smallest division on themainscale
So, V.C. =
Totalno. of divisionssonthe Vernierscale
When the body is placed between the two jaws A and B of a Vernier Calliper, suppose the main scale
reading is x. If n is the number of vernier scale division coinciding, then the observed reading is given as,
Observed reading = x + n (V.C.)

After measuring the internal diameter and depth of a beaker or a calorimeter, we can fi nd its volume as,
Volume of a beaker or a calorimeter = V = Internal area of cross-section × Depth

2
V = d 2 × h or V= πdh

2 4
where d is the internal diameter of a beaker or a calorimeter, and
h is the depth of a beaker or a calorimeter.

Procedure
(i) Measurement of Diameter of a Cylindrical body or Spherical body
1. Determine the least count or Vernier constant (V.C.) of the Vernier Calliper.

2. Bring the movable jaw BD in close contact with the fi xed jaw AC and determine the zero error. Record
the zero error, if any.
3. Place the spherical or cylindrical body between C D S Main Scale (M) N
V
the two jaws AC and BD, and adjust the jaw BD 0 1 3 5 6 7 8 9 10
so that it gently grips the body between the two P
jaws. Now, tighten the screw S.

4. Note the main scale reading (the position of zero
mark of the Vernier scale V on the main scale). For A B
this, record the main scale reading just before the Sphere
zero mark of the Vernier scale. This reading x is Fig. 1.2: Vernier Calliper-measuring
called main scale reading (M.S.R.). diameter of a spherical body
5. Note the number of Vernier scale division (n) which coincides with some division of the main scale.

The coinciding number is to be counted from the zero end of Vernier scale.
6. Calculate the product of n and V.C., y which is called Vernier scale reading (V.S.R.). Now, add V.S.R.
and M.S.R. to obtain diameter of the spherical or cylindrical body.

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