Question

The length of two rods measured by a meter scale are $60.0 \mathrm{cm}$ and $20.0 \mathrm{cm}$ respectively. The least count of meter scale is 1 mm. Then
This question has multiple correct options
(A) First measurement is more accurate
(B) Second measurement is more accurate
(C) Both measurements are equally accurate
(D) First measurement is more is more precise

Answer 1

Hint: We should 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. The Vernier calliper least count formula is calculated by dividing the smallest reading of the main scale with the total number of divisions of the vernier scale. Least Count 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. Based on this concept we have to answer this question.

Complete step by step answer:
Given scale is a meter scale, that means it has a count of $1000 \mathrm{mm}$ with a resolution of 1
$\mathrm{mm}$
Accuracy is $100 \%$ if one says the reading is $600 \mathrm{mm}$ or $200 \mathrm{mm},$ but an information is lost every time in moving the most significant digit or in scale conversion. It can be $599 \mathrm{mm}$ but we round it to $60 \mathrm{cm}$. It depends on our adaption of that flexibility in rounding off the value. We say it $\boldsymbol{x} \%$ of fsd [full scale reading].
Accuracy = (How much the fsd is scaled by the reading)$\times$(x) %
Here, Accuracy $=\dfrac{1000}{600\text{ or }200}\times x%$
and if the least count is $1 \mathrm{cm}$,
$\text{ Accuracy }=\dfrac{100}{60\text{ or }20}\times x%$
So, both $60 \mathrm{cm}$ and $20 \mathrm{cm}$ are not reliable until it is explicitly said $600 \mathrm{mm}$ or $200 \mathrm{mm}$.

Therefore, the correct answer is Option C.

Note: We should know that the vernier callipers found in the laboratory incorporates a main scale and a sliding vernier scale which allows readings to the nearest 0.02 mm. This instrument may be used to measure outer dimensions of objects (using the main jaws), inside dimensions (using the smaller jaws at the top), and depths (using the stem). Vernier calliper is an instrument that is used to measure internal and external dimensions and distances. Vernier callipers can measure accuracy to one-hundredth of a millimetre and one thousand of an inch. With a vernier calliper, you can make more precise measurements than you could with regular rulers.
It should also be known as vernier height gauges employ the use of a main scale and a Vernier scale to provide for greater resolution of the measured value. They are generally available in measuring size ranges from 6 inches to 6 feet. Models can have imperial (inch) or metric (mm) scales or both on them.