Assertion: Angle and angular displacement a dimensionless quantities.
Reason: Angle is equal in arc length divided by radius.

Options

A. if both assertion and reason are true reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation fo assertion.
C. If assertion is true but reaso is false.
D. IF both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason about angles and angular displacement, we can break it down into clear steps:

### Step 1: Understand the Assertion
The assertion states that "Angle and angular displacement are dimensionless quantities." To analyze this, we need to consider the definitions of angle and angular displacement.

### Step 2: Definition of Angular Displacement
Angular displacement (θ) is defined as the angle through which an object has rotated about a fixed point. It is often measured in radians.

### Step 3: Relationship Between Arc Length and Radius
The reason provided states that "Angle is equal to arc length divided by radius." Mathematically, this is expressed as:
\[ \theta = \frac{s}{r} \]
where:
- \( \theta \) is the angular displacement in radians,
- \( s \) is the arc length,
- \( r \) is the radius of the circle.

### Step 4: Analyze Dimensions
In the equation \( \theta = \frac{s}{r} \):
- The dimension of arc length \( s \) is [L] (length).
- The dimension of radius \( r \) is also [L] (length).

When we divide arc length by radius:
\[ \frac{s}{r} = \frac{[L]}{[L]} = 1 \]
This means that the angle \( \theta \) is dimensionless, as it has no units.

### Step 5: Conclusion on the Assertion
Since we have shown that angular displacement is indeed dimensionless, the assertion is correct.

### Step 6: Analyze the Reason
The reason states that "Angle is equal to arc length divided by radius." This statement is also true as we derived it from the definition of angular displacement.

### Step 7: Relationship Between Assertion and Reason
While both the assertion and the reason are true, the reason does not provide a correct explanation for why angles are dimensionless. It merely states a relationship. Therefore, while the reason is true, it does not justify the assertion.

### Final Conclusion
Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion.