Three charges +q, +2q and 4q are connected by strings as shown in the figure and are in equilibrium. What is ratio of tensions in the strings AB and BC?

Let's analyze the forces acting on each charge using Coulomb's law. According to Coulomb's law, the electric force F between two charges q₁ and q₂ separated by a distance r is given by:

F = (k * q₁ * q₂) / r²

where k is Coulomb's constant, with a value of approximately 9 × 10⁹ Nm²/C².

Step 1: Identifying the Charges and Distances

We have three charges, q₁ = +q, q₂ = +2q, and q₃ = +4q, separated by equal distances d as shown in the figure.

Step 2: Analyzing the Tension in String AB

Assuming the system is in equilibrium, the tension in the string AB (let's call this tension T_AB) will balance the electrical force exerted on charge A by charges B and C. Hence:

T_AB = E_A

The electric force on charge A, denoted as E_A, is calculated as follows:

E_A = k[(2q * q) / d² + (4q * q) / (4d²)]

Simplifying the above expression:

E_A = k[(2q²) / d² + (4q²) / (4d²)] = (3kq²) / d²

Thus, T_AB = (3kq²) / d².

Step 3: Analyzing the Tension in String BC

Similarly, the tension in string BC (T_BC) will balance the electrical forces on charge C. Therefore:

T_BC = E_C

The electric force on charge C, E_C, is given by:

E_C = k[(8q²) / d² + (4q²) / (4d²)]

Simplifying further:

E_C = (9kq²) / d²

Thus, T_BC = (9kq²) / d².

Step 4: Finding the Ratio of Tensions T_AB and T_BC

Now, we calculate the ratio of the tensions in strings AB and BC:

(T_AB) / (T_BC) = [(3kq²) / d²] / [(9kq²) / d²] = 1 / 3

Therefore, the ratio of tensions in strings AB and BC is 1:3.

Conclusion:

The correct answer is Option B: 1:3.

Note:

The electric force between two charges can be attractive or repulsive depending on the nature of the charges. Here, since all charges are positive, they repel each other, resulting in equilibrium tensions in the connecting strings.