Assertion : If a particle is projected from the surface of earth with velocity equal to escape velocity, then total mechanical energy is zero
Reason : Total mechanical energy of any closed system is always negative.

Options

A. If both Assertin 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 given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
- Escape velocity is the minimum velocity required for an object to break free from the gravitational attraction of a celestial body (in this case, Earth) without any further propulsion.
- The formula for escape velocity \( V_e \) from the surface of the Earth is given by:
\[ V_e = \sqrt{\frac{2GM}{R}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( R \) is the radius of the Earth.

2. **Total Mechanical Energy at Escape Velocity**:
- The total mechanical energy \( E \) of an object in a gravitational field is given by the sum of its kinetic energy \( KE \) and potential energy \( PE \):
\[ E = KE + PE \]
- At escape velocity, the kinetic energy \( KE \) is:
\[ KE = \frac{1}{2}mv^2 = \frac{1}{2}mV_e^2 \]
- The potential energy \( PE \) at the surface of the Earth is:
\[ PE = -\frac{GMm}{R} \]
- Substituting the escape velocity into the kinetic energy equation:
\[ KE = \frac{1}{2}m\left(\sqrt{\frac{2GM}{R}}\right)^2 = \frac{1}{2}m\left(\frac{2GM}{R}\right) = \frac{GMm}{R} \]

3. **Calculating Total Mechanical Energy**:
- Now, substituting \( KE \) and \( PE \) into the total mechanical energy equation:
\[ E = \frac{GMm}{R} - \frac{GMm}{R} = 0 \]
- Thus, the total mechanical energy when a particle is projected with escape velocity is indeed zero.

4. **Evaluating the Assertion**:
- The assertion states that if a particle is projected from the surface of the Earth with velocity equal to escape velocity, then the total mechanical energy is zero. This is **true** based on our calculation.

5. **Evaluating the Reason**:
- The reason states that the total mechanical energy of any closed system is always negative. This statement is **not true**. The total mechanical energy can be zero (as in the case of escape velocity) or positive, depending on the system and the conditions.
- Therefore, while the reason is true in some contexts, it does not correctly explain the assertion.

6. **Conclusion**:
- Both the assertion and reason are correct statements, but the reason is not a correct explanation of the assertion. Thus, the correct answer is that the assertion is true, but the reason is not a valid explanation.

### Final Answer:
- The assertion is true, and the reason is false. Therefore, the correct option is that both the assertion and reason are correct, but the reason is not the correct explanation of the assertion.