Assertion : The condition of equilibrium for a rigid body is
Translational equilibrium `Sigma F=0` and
Rotational equilibrium `Sigma tau=0`
Reason : A rigid body musy be in equilibrium under the action of two equal and opposite forces.

Options

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

Answer

To solve the assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understand the Assertion
The assertion states that the condition for equilibrium of a rigid body includes:
1. **Translational Equilibrium**: This is represented by the equation \( \Sigma F = 0 \), meaning that the sum of all forces acting on the body must be zero.
2. **Rotational Equilibrium**: This is represented by the equation \( \Sigma \tau = 0 \), meaning that the sum of all torques acting on the body must also be zero.

**Conclusion**: The assertion is correct.

### Step 2: Understand the Reason
The reason states that a rigid body must be in equilibrium under the action of two equal and opposite forces.

- When two equal and opposite forces act on a rigid body, they do indeed result in translational equilibrium because the forces cancel each other out, leading to \( \Sigma F = 0 \).
- However, these two forces can create a torque about a point if they are not acting through the same line (i.e., they are separated by a distance \( d \)). The torque \( \tau \) is calculated as \( \tau = F \cdot d \), where \( F \) is the magnitude of one of the forces and \( d \) is the distance between the lines of action of the forces.

**Conclusion**: While the two forces can satisfy translational equilibrium, they do not guarantee rotational equilibrium because they can produce a net torque.

### Step 3: Final Evaluation
- The assertion is true: A rigid body must satisfy both translational and rotational equilibrium conditions to be in complete equilibrium.
- The reason is false: While two equal and opposite forces can lead to translational equilibrium, they do not ensure rotational equilibrium if they create a torque.

### Final Answer
The assertion is true, but the reason is false.