Question

If the distance is measured in kilometre scale, then the maximum permissible error will be:
(A) $ {10^{ - 3}} $ on mm scale
(B) $ {10^6} $ on mm scale
(C) $ {10^3} $ on mm scale
(D) $ {10^7} $ on mm scale

Answer 1

Hint To find the error in the measurement, we need to use the least count of a kilometre scale. Least count is calculated by dividing the main scale reading by the total number of divisions in the main scale.

Formula Used: In this solution we will be using the following formula,
$\Rightarrow L.C = \dfrac{{{\text{Smallest division on main scale}}}}{{{\text{Total number of divisions}}}} $
where $ L.C $ is the least count.

Complete step by step answer
The total number of divisions of a kilometre scale is 1000 divisions of metres. So the smallest division on the kilometre scale will be 1 meter.
So, the least count of the scale can be calculated by the formula,
 $\Rightarrow L.C = \dfrac{{{\text{Smallest division on main scale}}}}{{{\text{Total number of divisions}}}} $
Substituting the values we get,
 $\Rightarrow L.C = \dfrac{1}{{1000}}m $
On calculating this gives us,
 $\Rightarrow L.C = 0.001m $
which is equal to 1mm.
Now, as in the question, we need to calculate in terms of millimetre.
The conversion factor from kilometre to meter is, $ 1km = {10^6}mm $
Thus, the least count of kilometer scale will be $ {10^6} $ on mm scale.
Hence, the correct answer is option B.

Additional Information
There are many ways to reduce the errors that are caused in measurement. Some of them are:
-We can take two or more measurements and then double check them.
-We can use a different measuring instrument for measuring the same quantity.

Note
The least count of a device is the smallest amount that can be measured by that device. It is also used to see the precision of an instrument. The instrument that has a smaller value of least count can measure a smaller value and hence is more precise.