Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).

Assertion (A): At a given moisture content, grain angle of repose is equal to the angle of internal friction
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:

Be careful with the wording of trigonometric definitions:
The coefficient of friction is the tangent of the angle (\(\mu = \tan\phi\)).
The angle is the inverse tangent of the coefficient (\(\phi = \arctan\mu\)).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Granular materials exhibit shear strength and frictional resistance that can be represented by the angle of internal friction and the static angle of repose.

Step 3: Detailed Explanation:
1.

Assertion (A): For dry or moderately moist cohesionless granular materials (like grains), the angle of repose is practically equal to the angle of internal friction of the material. Thus, Assertion (A) is true.
2.

Reason (R): By definition, the coefficient of friction (\(\mu\)) is equal to the tangent of the angle of friction (\(\phi\)):
\[ \mu = \tan\phi \] Solving for the angle:
\[ \phi = \tan^{-1}(\mu) \quad (\text{arctangent of the coefficient}) \] The statement incorrectly states that the angle is equal to the "tangent of the coefficient of friction" (\(\phi = \tan\mu\)), which is mathematically incorrect and conceptually invalid. Thus, Reason (R) is false.

Step 4: Final Answer:
The correct option is 3, which corresponds to (A) is true but (R) is false.