Question

The diameter of a steel ball is measured using Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as.

S. No.	MS(cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is -0.03 cm, then the mean corrected diameter is.
A. 0.56
B. 0.53
C. 0.52
D. 0.59

Answer 1

Hint: We will firstly found the least count of Vernier caliper then we will use the formula to find the reading of the scale .after that we will find three readings and after that, we will take the mean of three readings and find the mean diameter.

Formula used:
L.C.=1M.S.D.−1V.S.D.
The reading of scale is given as Main Scale reading + L.C.×VSD−error

Complete step by step answer:
The following figure shows the vernier calipers and all its parts:

The LC of vernier calipers is given as
 L.C.=1M.S.D.−1V.S.D.

We know that where MSD and VSD are main and vernier scale division:
MSD=0.1 cm


We are Given 10 VSD coincides with 9 MSD then,

\[10VSD=9MSD=VSD=0.9MSD=0.09cm\]


The least count is given as
\[0.1~cm-0.09~cm~=0.01~cm\]
We will find the reading of scales,

The reading of scale is given as Main Scale reading + L.C.×VSD−error

\[\begin{align}
  & Reading\text{ }1~=0.5~cm+0.01\times 8-\left( -0.03 \right)~cm~=0.61~cm \\
 & Reading\text{ }2~=0.5~cm+0.01\times 4-\left( -0.03 \right)~cm~=0.57~cm \\
 & Reading\text{ }3~=0.5~cm+0.01\times 6-\left( -0.03 \right)~cm~=0.59~cm \\
\end{align}\]


Taking an average of three readings diameter

\[=\dfrac{0.61+0.57+0.59}{3}=0.59cm\]

The mean corrected diameter is 0.59cm.

The correct option is (D)

Additional Information:
We know that the smallest amount count gives the resolution of the instrument. Also, an Ammeter or Voltmeter is claimed to possess zero error. When their pointer doesn't read zero when it's alleged to read i.e. when not connected to the circuit.
Let us see what's vernier micrometer. Vernier caliper may be a device that is employed to live small lengths and distances like the diameter of a cylinder or sphere with the assistance of a vernier micrometer we will calculate correctly up to 0.1mm. Also, the difference between the worth of 1 main scale division and one vernier division is named as “Least count (L.C) or vernier constant (V.C)”.

Note:
The least Count of an instrument is the smallest value which will be measured by using that instrument.
The least count of an instrument features a direct relationship with the accuracy and precision of that instrument. Most of the vernier Calipers have a least count of 0.1mm.
To get the smallest amount count of the "main scale", count the number of divisions on the most scale in one cm of it. Divide 1 cm into that much number of divisions; the worth obtained is that the least count of the most scales in cm.