STATEMENT-1 `:` In a meter bridge, if its wire is replaced by another wire having same length, same material but twice the cross sectional area, then the accuracy of measurement decreases.
and
STATEMENT-2 `:` Accuracy of meter bridge depends on the length of wire.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is True
D. Statement-1 is False , Statement-2 is True

Answer

To solve the problem, we need to analyze both statements regarding the meter bridge and its accuracy.

### Step 1: Understand the Principle of the Meter Bridge
The meter bridge operates on the principle of the Wheatstone bridge, which is based on the balance of two legs of a circuit. The resistances in the meter bridge are compared using the lengths of wire.

**Hint:** Recall that the meter bridge is used to measure unknown resistances by balancing two arms of the bridge.

### Step 2: Analyze Statement 1
Statement 1 claims that if the wire in a meter bridge is replaced with another wire of the same length and material but with twice the cross-sectional area, the accuracy of measurement decreases.

The resistance \( R \) of a wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area. If the area \( A \) is doubled, the resistance will be halved. However, since the meter bridge measures the ratio of resistances, the effect of the cross-sectional area cancels out when comparing resistances.

**Hint:** Consider how the resistance changes when the cross-sectional area is altered and how this affects the balance in the meter bridge.

### Step 3: Analyze Statement 2
Statement 2 states that the accuracy of the meter bridge depends on the length of the wire.

The accuracy of the meter bridge is indeed influenced by the length of the wire. A longer wire allows for smaller changes in resistance to be detected, which increases the precision of the measurement. If the length is decreased, the potential gradient (voltage per unit length) increases, allowing for finer measurements.

**Hint:** Think about how the length of the wire affects the potential difference and the ability to measure small changes.

### Step 4: Conclusion
From the analysis:
- Statement 1 is **false** because the accuracy does not decrease with a change in cross-sectional area.
- Statement 2 is **true** because the accuracy is indeed dependent on the length of the wire.

Thus, the correct conclusion is that Statement 1 is false and Statement 2 is true.

**Final Answer:** Statement 1 is false, and Statement 2 is true.