To solve this problem, we need to understand how a meter bridge works and how the balance condition is established in the circuit. The meter bridge is based on the principle of the Wheatstone bridge, which states that the ratio of the resistances is equal to the ratio of the lengths of the wire when the bridge is balanced.

Understanding the Initial Setup

In the initial scenario, we have a meter bridge with the following parameters:

• Length of the bridge (AB) = 100 cm
• Length to the jockey position (X) = 12 cm
• Resistance R = 18 ohms
• Resistance X = unknown

When the jockey is at position X, the bridge is balanced, meaning:

R / X = (100 - X) / X

Substituting the known values:

18 / X = (100 - 12) / 12

This simplifies to:

18 / X = 88 / 12

Cross-multiplying gives:

18 * 12 = 88 * X

From this, we can find the value of X:

X = (18 * 12) / 88 = 2.45 ohms

Changing the Resistance

Now, we change the resistance R to 8 ohms and need to find the new position of the jockey for balance. The new balance condition can be expressed as:

R' / X' = (100 - X') / X'

Where R' is the new resistance (8 ohms) and X' is the new length to the jockey position. We can set up the equation:

8 / X' = (100 - X') / X'

Cross-multiplying gives:

8 * X' = (100 - X') * X'

Rearranging this leads to:

8 * X' = 100 * X' - (X')^2

Bringing all terms to one side results in:

(X')^2 - 92 * X' = 0

Factoring out X' gives:

X' (X' - 92) = 0

This means X' can either be 0 or 92 cm. Since we are looking for a physical position, we take X' = 92 cm.

Calculating the Distance Moved

Initially, the jockey was at 12 cm. Now, it needs to be at 92 cm for balance with the new resistance. The distance moved by the jockey is:

Distance moved = New position - Initial position = 92 cm - 12 cm = 80 cm

Final Thoughts

However, it seems we need to find the distance moved from the original balance point to the new balance point, which is not directly listed in the options provided. If we consider the options given (10 cm, 20 cm, 30 cm, 40 cm), it appears that there may be a misunderstanding in the problem setup or the options themselves. Based on our calculations, the jockey would need to move significantly more than any of the provided options to achieve balance with the new resistance.