The smallest division on the main scale of a Vernier calipers is $01 \,cm$ Ten divisions of the Vernier scale correspond to nine divisions of the main scale The figure below on the left shows the reading of this calipers with no gap between its two jaws The figure on the right shows the reading with a solid sphere held between the jaws The correct diameter of the sphere is
- 3.07 cm
- 3.11 cm
- 3.15 cm
- 3.17 cm
The Correct Option is C
Solution and Explanation
Step 1: Identify the least count (L.C) of the Vernier calipers
The least count is the smallest measurement that can be accurately read using the instrument. It is given as:
L.C = 0.01 cm
This means the Vernier calipers can measure up to one-hundredth of a centimeter accurately.
Step 2: Account for the systematic error
Sometimes, the instrument may have a zero error or a systematic error due to misalignment or calibration issues. In this case, it is given that there is an error equivalent to 4 least counts:
Error = 4 × L.C = 4 × 0.01 cm = 0.04 cm
This error needs to be added to the observed measurement to obtain the true value.
Step 3: Determine the observed reading
The observed measurement from the Vernier calipers consists of two parts:
- Main scale reading = 3.1 cm
- Vernier scale reading = 1 division = 1 × 0.01 cm = 0.01 cm
So, Observed reading = 3.1 cm + 0.01 cm = 3.11 cm
Step 4: Add the error to get the corrected value
To get the correct diameter of the sphere, the error is added to the observed value:
Corrected diameter = 3.11 cm + 0.04 cm = 3.15 cm
Final Answer:
Therefore, the correct diameter of the sphere is 3.15 cm
Correct option: Option (C)
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Concepts Used:
Units and Measurement
Unit:
A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.
Measurement:
The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
Read More: Fundamental and Derived Units of Measurement
System of Units:
- CGS system
- FPS system
- MKS system
- SI units
Types of Units:
Fundamental Units -
The units defined for the fundamental quantities are called fundamental units.
Derived Units -
The units of all other physical quantities which are derived from the fundamental units are called the derived units.