Assertion (A): The balancing point of a meter bridge is obtained at L = 40 cm. When the area of cross-section of the wire of is doubled, the balancing point shifts to L = 60 cm.
Reason (R ): Resistance of wire is directly proportional to its area of cross-section.

Options

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 and R is true

Explanation

To solve the given question, we need to analyze both the Assertion (A) and Reason (R) provided in the question.

### Step 1: Analyze the Assertion (A)
The assertion states that the balancing point of a meter bridge is obtained at \( L = 40 \, \text{cm} \). When the area of cross-section of the wire is doubled, the balancing point shifts to \( L = 60 \, \text{cm} \).

In a meter bridge, the balancing point is determined by the ratio of the resistances connected in the two gaps of the bridge. The formula for the balancing point is given by:

\[ \frac{R}{X} = \frac{L}{100 - L} \]

where \( R \) is the resistance in one gap, \( X \) is the resistance in the other gap, and \( L \) is the length of the bridge from one end to the balancing point.

The balancing point \( L \) depends on the resistances \( R \) and \( X \), but it does not depend on the area of cross-section of the wire. Thus, the assertion that the balancing point shifts due to the change in area of cross-section is incorrect.

**Conclusion for Assertion (A):** False

### Step 2: Analyze the Reason (R)
The reason states that the resistance of a wire is directly proportional to its area of cross-section.

The resistance \( R \) of a wire is given by the formula:

\[ R = \rho \frac{L}{A} \]

where \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is the area of cross-section. From this formula, we can see that resistance is inversely proportional to the area of cross-section \( A \) (i.e., \( R \propto \frac{1}{A} \)). Therefore, the statement that resistance is directly proportional to the area of cross-section is incorrect.

**Conclusion for Reason (R):** False

### Final Conclusion
Both the Assertion (A) and Reason (R) are false.

### Summary of the Solution
- Assertion (A): False
- Reason (R): False