In a meter bridge experiment, null point is obtained at `20 cm` from one end of the wire when resistance `X` is balanced against another resistance `Y`. If `X lt Y`, then the new position of the null point from the same end, if one decides to balance a resistance of `4 X` against `Y` will be at.

Options

A. `50 cm`
B. `80 cm`
C. `40 cm`
D. `70 cm`

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the meter bridge principle
In a meter bridge experiment, the balance point (null point) is determined by the ratio of the resistances. The formula used is:
\[ \frac{X}{Y} = \frac{L}{100 - L} \]
where \(L\) is the distance from one end of the bridge wire to the null point.

### Step 2: Set up the first case
From the problem, we know that when resistance \(X\) is balanced against resistance \(Y\), the null point is at \(20 \, \text{cm}\) from one end of the wire. Therefore, we can write:
\[ \frac{X}{Y} = \frac{20}{100 - 20} = \frac{20}{80} = \frac{1}{4} \]

### Step 3: Set up the second case
Now, we need to find the new position of the null point when \(4X\) is balanced against \(Y\). We can denote the new null point as \(L\). The relationship can be expressed as:
\[ \frac{4X}{Y} = \frac{L}{100 - L} \]

### Step 4: Substitute the known ratio
From the first case, we know that \(\frac{X}{Y} = \frac{1}{4}\). Therefore, we can express \(4X\) in terms of \(Y\):
\[ \frac{4X}{Y} = 4 \cdot \frac{X}{Y} = 4 \cdot \frac{1}{4} = 1 \]
Thus, we can rewrite the equation:
\[ 1 = \frac{L}{100 - L} \]

### Step 5: Solve for \(L\)
Cross-multiplying gives us:
\[ 100 - L = L \]
Adding \(L\) to both sides results in:
\[ 100 = 2L \]
Dividing both sides by \(2\) gives:
\[ L = 50 \, \text{cm} \]

### Conclusion
Therefore, the new position of the null point from the same end, when balancing resistance \(4X\) against \(Y\), will be at \(50 \, \text{cm}\).