Question

Following statements are made with respect to the mass curve of rainfall:
(I) Slope at a point on the curve can be positive.
(II) Slope at a point on the curve can be zero.
Which one of the following options is CORRECT?

• A. Both statements (I) and (II) are TRUE.
• B. Both statements (I) and (II) are FALSE.
• C. Statement (I) is TRUE and statement (II) is FALSE.
• D. Statement (I) is FALSE and statement (II) is TRUE.

Hint:

The slope of a rainfall mass curve equals the instantaneous rainfall intensity, which is zero in dry spells and positive while raining, but never negative.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept.
A mass curve of rainfall is a plot of cumulative (running total) rainfall against time. At any instant the reading on the curve is the sum of all rainfall that has fallen up to that time, so the curve can never come back down; it is a non-decreasing curve by construction.

Step 2: Key relationship between slope and rainfall intensity.
The slope of the mass curve at any point equals the instantaneous rainfall intensity there, \(i=\dfrac{d(\text{cumulative rainfall})}{dt}\). Rainfall intensity can only be zero (no rain falling right then) or positive (rain actively falling); it can never be negative, since rainfall cannot un-fall.

Step 3: Detailed Explanation of each statement.
Statement (I): during any interval when rain is actively falling, the cumulative total keeps climbing, so the slope at that point is positive, matching the rainfall intensity at that instant. TRUE.
Statement (II): during a dry spell between two rain bursts, the cumulative total stays flat since no new rainfall is being added, so the curve is horizontal there with slope exactly zero. Also TRUE.
Because the curve is never allowed to decrease, a negative slope never occurs; the only two possibilities anywhere on the curve are a positive slope while raining or a zero slope in a dry period, exactly what the two statements describe.

Step 4: Final Answer.
Both statements are consistent with how a mass curve of rainfall behaves. \[ \boxed{\text{Both statements (I) and (II) are TRUE}} \]