To determine the least count of an instrument used for rainfall determination, we need to understand the concept of least count and how it is calculated.

What is Least Count?
The least count of an instrument is the smallest value that can be measured using that instrument. It represents the level of accuracy and precision with which measurements can be made.

Formula for Least Count:
The formula to calculate the least count is given by:
Least Count = (Smallest division on the scale) / (Total number of divisions on the scale)

Given Data:
Volume of the bucket (V) = 50 cu. m
Area of the funnel (A) = 21 sq. m

Calculating the Least Count:
1. Volume of water collected in the bucket:
The volume of water collected in the bucket is equal to the volume of rainfall. Therefore, the volume can be calculated as:
Volume = V / A
Volume = 50 cu. m / 21 sq. m
Volume = 2.38 cu. m

2. Smallest division on the scale:
The smallest division on the scale is the smallest increment that can be measured on the instrument. In this case, the smallest division is the smallest increment of volume that can be measured. Since the volume is 2.38 cu. m, the smallest division can be taken as 0.01 cu. m.

3. Total number of divisions on the scale:
The total number of divisions on the scale represents the number of increments that can be measured on the instrument. In this case, since the smallest division is 0.01 cu. m, the total number of divisions can be calculated as:
Total number of divisions = Volume / Smallest division
Total number of divisions = 2.38 cu. m / 0.01 cu. m
Total number of divisions = 238

4. Calculating the Least Count:
Using the formula for least count, we can substitute the values:
Least Count = Smallest division / Total number of divisions
Least Count = 0.01 cu. m / 238
Least Count = 0.000042 cu. m

Answer:
Therefore, the least count of the instrument used for rainfall determination is 2.38 m.