Assertion : Two identical balls are charged by q. They are suspended from a common point by two insulating threads l each. In equilibrium, the angle between the tension in the threads is `180^(@)`. (Ignore gravity).
Reason : In equilibrium tension in the spring is
`T=1/(4pi epsi_(0)) (q.q)/l^(2)`

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true

Answer

To solve the problem step by step, we will analyze the assertion and the reason provided in the question.

### Step 1: Understanding the Assertion
The assertion states that two identical balls, each charged with charge \( q \), are suspended from a common point by two insulating threads of length \( l \). In equilibrium, the angle between the tensions in the threads is \( 180^\circ \).

- Since both balls are identical and have the same charge, they will repel each other due to electrostatic forces.
- In equilibrium, the only forces acting on each ball are the tension in the thread and the electrostatic force of repulsion between the two charged balls.
- The configuration where the angle between the threads is \( 180^\circ \) means that the balls are directly opposite each other, maximizing the distance between them, which is consistent with the repulsive force.

### Conclusion for Step 1
The assertion is **correct** because in equilibrium, the angle between the tensions in the threads can indeed be \( 180^\circ \) when gravity is ignored.

### Step 2: Analyzing the Reason
The reason states that in equilibrium, the tension in the spring (or thread) is given by the formula:
\[ T = \frac{1}{4\pi \epsilon_0} \frac{q \cdot q}{l^2} \]

- The electrostatic force \( F_E \) between the two charges \( q \) separated by a distance \( r \) is given by Coulomb's law:
\[ F_E = \frac{1}{4\pi \epsilon_0} \frac{q^2}{r^2} \]
- In this case, since the balls are at a distance of \( 2l \) apart (each thread has length \( l \)), the distance \( r = 2l \).
- Therefore, the electrostatic force becomes:
\[ F_E = \frac{1}{4\pi \epsilon_0} \frac{q^2}{(2l)^2} = \frac{1}{4\pi \epsilon_0} \frac{q^2}{4l^2} = \frac{1}{16\pi \epsilon_0} \frac{q^2}{l^2} \]

### Conclusion for Step 2
The tension \( T \) in the thread must equal the electrostatic force \( F_E \) in equilibrium:
\[ T = F_E = \frac{1}{16\pi \epsilon_0} \frac{q^2}{l^2} \]
Thus, the reason provided in the question is **incorrect** because it does not account for the correct distance between the charges.

### Final Conclusion
- The assertion is **true**.
- The reason is **false**.