Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : The angle of repose is generally higher than angle of the internal friction for the grains of approximately the same moisture content and density.
Reason (R) : The angle of internal friction is equal to the tangent of coefficient of friction for the material.
In light of the above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Hint:

Always check the wording of mathematical definitions in Reason statements. The coefficient of friction is equal to the tangent of the angle (\(\mu = \tan\theta\)), which means the angle itself is the inverse tangent (\(\theta = \tan^{-1}\mu\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question tests definitions of physical properties of granular materials: the angle of repose and the angle of internal friction. Both characterize the flow and shearing properties of bulk solids.

Step 2: Detailed Explanation:
Let us evaluate each statement:

Assertion (A): The angle of repose is the maximum angle of the slope at which a pile of loose granular material remains stable without sliding.
The angle of internal friction is the angle on a Mohr-Coulomb shear failure envelope, representing the resistance to shear within the grain mass.
For most grains, during free pouring, the surface layers are loose and have less interlocking than the internal compacted grains.
However, under standard test conditions, the static angle of repose (especially for moist or cohesive grains) can be higher than the internal friction angle due to surface tension, cohesion, and moisture bridging effects.
Conversely, for dry, free-flowing grains, the angle of repose is approximately equal to or slightly smaller than the internal friction angle.
In standard agricultural engineering literature, the assertion is accepted as generally true for standard grain conditions. Thus, Assertion (A) istrue.

Reason (R): The relationship between the coefficient of internal friction (\(\mu\)) and the angle of internal friction (\(\theta\)) is: \[ \mu = \tan\theta \] Taking the inverse tangent of both sides: \[ \theta = \tan^{-1}\mu \] This means the angle of internal friction is equal to theinverse tangent (or arctangent) of the coefficient of friction.
The statement claims that the angle is equal to the "tangent of the coefficient of friction" (\(\theta = \tan\mu\)), which is mathematically incorrect and conceptually flawed. Thus, Reason (R) isfalse.
Thus, Assertion (A) is true but Reason (R) is false.

Step 3: Final Answer:
The correct option is (C), which indicates that (A) is true but (R) is false.