1. Interpret the circuit

A rectangular loop $PQRS$ is made of uniform wire.

Given:

• $PQ = RS = 100\,\text{cm} = 1\,\text{m}$
• $PR = QS = 5\,\text{cm}$ means the vertical separation between the long sides $PQ$ and $RS$ is $5\,\text{cm} = 0.05\,\text{m}$.

The force per unit length on wire $PQ$ due to wire $RS$ is the force between two parallel current-carrying wires:

where $d$ is the separation, and $I_1, I_2$ are currents in the two parallel segments.

So we need the currents in sides $PQ$ and $RS$ when the ammeter reading changes from $I$ to $2I$.

2. Resistance ratio of the two branches

Since the wire is uniform, resistance is proportional to length.

Between points $P$ and $Q$, there are two paths:

• Direct path $PQ$ of length $100\,\text{cm}$
• Other path $P \to S \to R \to Q$ of total length $5 + 100 + 5 = 110\,\text{cm}$

Thus resistances are in ratio

Let

If total current through the loop (ammeter reading) is $I_{\text{tot}}$, it divides inversely to resistance:

Hence,

The current in wire $RS$ is same as the current in the branch $PSRQ$, so

3. Force per unit length when ammeter reads $I$

If ammeter reading is $I$, then

Therefore,

So,

4. Force per unit length when ammeter reads $2I$

Now total current becomes $2I$.

Current division ratio remains same, so

Hence,

Therefore,

5. Check options

• A: $1:4$ ✅
• B: $1:3$ ❌
• C: $1:2$ ❌
• D: $1:5$ ❌

So the correct answer is A.