Question

The diameter of wire measured with a Vernier calliper with least count 0.1 mm is S cm, then the percentage error in measurement is
(A) 0.2%
(B) 2%
(C) 5%
(D) 0.5%

Answer 1

Hint: We know that the smallest value that can be measured by the measuring instrument is called its least count. Measured values are good only up to this value. The least count error is the error associated with the resolution of the instrument. A metre ruler may have graduations at 1 mm division scale spacing or interval. Pitch = Unit of main scale/No. of divisions in the unit for example If the unit of the main scale is centimetres & the number of divisions is 10 then pitch 0.1. Least count is the magnitude of the smallest measurement that can be measured by an instrument accurately.

Complete step-by step answer:
It is known to us that vernier calliper least counts formula is calculated by dividing the smallest reading of the main scale with the total number of divisions of the vernier scale. LC of vernier calliper is the difference between one smallest reading of the main scale and one smallest reading of vernier scale which is 0.1 mm 0r 0.01 cm.
We know that the least count is = 0.01 cm
Error = + 0.02 cm = which is the positive count
Error = + 0.02 cm
Main scale reading (MSR) 3.60 cm 8th Vernier scale coincides with main scale $\Rightarrow$Vernier coincidence (VC) = 8
We know that,
Correct diameter is given as = [main scale reading (LC $\times$V.C)-(error)]
$=\left[ 3.60+\left( 0.01\times 8 \right)-\left( +0.002 \right) \right]$
$=\left( 3.60+0.08 \right)-\left( +0.02 \right)$
$\,\,=3.68-0.02$
$=3.66\,cm$
$\dfrac{diameter}{2}=\dfrac{3.66}{2}$correct radius is =$\dfrac{diameter}{2}=\dfrac{3.66}{2}$
$=1.83\,cm$

Hence, the correct answer is Option C.

Note: We know that the main scale reading is the first reading on the main scale immediately to the left of the zero of the vernier scale (3 mm), while the vernier scale reading is the mark on the vernier scale which exactly coincides with a mark on the main scale (0.7 mm). The main scale is used to know the whole and decimal numbers. After putting the object, read the main scale lined up with the sliding scale zero.
It should be known to us that the principle of vernier callipers is by a small amount to make fine measurements. The human eye can easily detect this alignment of lines which is the main fact that drives a vernier. Slightly displaced to the marks on the main scale. A Vernier Calliper is a precision instrument. It is designed to gauge the dimensions and depth of different objects. Vernier calliper is especially useful when it comes to measuring the diameter of circular objects such as cylinders. This is because its jaws can be perfectly secured on both sides of the circumference.