Question

A stop watch has 10 divisions graduated between the $0$ and $5s$marks. Its least count is $\dfrac{x}{2}$, find the value of $x$.

Answer 1

In order to solve this problem, we need to know that the least count of any instrument is the smallest value of measurement that can be measured using this instrument.

Complete answer:
Least count $= \dfrac{{range{\text{ }}of{\text{ }}reading}}{{number{\text{ }}of{\text{ }}divisions}}$
Least count of stopwatch$= \dfrac{{5 - 0}}{{10}} = 0.5\sec$ or $\dfrac{1}{2}$s.
Thus, the value of x is $1$.

Additional Information: 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 meter ruler may have graduations at 1 mm division scale spacing or interval.The values between the minimum measurable value and the maximum value that can be measured are called the range of the instrument. Set of values of quantities of the same kind that can be measured by a given measuring instrument or measuring system with specified instrumental uncertainty, under defined conditions. Or simply we can say that the range of measuring instruments is the maximum or minimum value an instrument can measure.

Note: While solving this question, one should have to know the concept of least count and how to calculate. The formula varies from instrument to instrument. Basic formula is mentioned above whereas one should be careful about the variables to be mentioned in the formula. For reference, the range of the scale is zero centimeter to thirty centimeters. Usually, we state the maximum value as the range since the minimum value is generally zero. When we say, the range of the meter scale is, we mean that the range is from zero to.