Question

Why is the use of zero error necessary for measuring instruments?

Answer 1

Hint: Least count of an instrument can be calculated by dividing the value of the main scale division by the total number of divisions on the scale of the instrument. To get the precise value through an instrument, its zero error should be calculated otherwise it will give wrong results.

Complete step-by-step answer:
If the zero of the main scale in the vernier calliper does not coincide with the zero of the vernier scale, then it is said that the instrument is having a zero error. Zero error is measured by calculating the distance between the main scale and the vernier scale. A zero error can be classified into two types. The first one is positive zero error and the second one is negative zero error.
The positive zero error in a vernier scale occurs when the zero of the vernier scale lies on the right-hand side of the main scale and the negative zero error in the vernier scale occurs when the zero of the vernier scale lies on the left of the main scale.
To find the positive zero error in the vernier scale, we first note down the division of the vernier scale which coincides with the division of the main scale, and then we will multiply the result by the least count of the instrument. Suppose the $$8^{th}$$ division of the vernier scale coincides with the division of the main scale then positive zero error will be given by.
$$\Rightarrow postivezeroerror=+8\times leastcount$$
To find the negative zero error in a vernier scale, we first note down the division of the vernier scale which coincides with the zero of the main scale, and then that division will be subtracted from the total number of divisions and then multiplied by the least count of the instrument. Suppose the total number of divisions is $$10$$ and the $$4^{th}$$ division coincides with the division of the vernier scale, then negative zero error will be given by.
$$\Rightarrow negativezeroerror=-(10-4)\times leastcount$$
zero error is necessary for measuring instruments to get accurate results and it also helps in checking the instrument whether it is working right or whether it is working wrong.

Note: The smallest and accurate value that can be measured on the scale of an instrument is known as the least count of the instrument. If an instrument is having a smaller value of least count then that instrument is more precise as compared to the instrument having a larger least count.