Which of the following statements are correct about a planet revolving around Sun ?

Answer

To determine which statements are correct about a planet revolving around the Sun, we will analyze the provided statements based on the principles of gravitation and orbital mechanics.

### Step-by-Step Solution:

1. **Understanding Total Mechanical Energy**:
- The total mechanical energy (E) of a planet in orbit is given by the formula:
\[ E = -\frac{GMm}{2r} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Sun, \( m \) is the mass of the planet, and \( r \) is the distance between the planet and the Sun.
- Since the total mechanical energy is negative, this indicates that the planet is in a bound state, which is correct.

2. **Orbit Shape**:
- The statement that the orbit of a planet must be circular is incorrect. According to Kepler's laws of planetary motion, planets can revolve in elliptical orbits, not just circular ones. Therefore, this statement is false.

3. **Leaving the Orbit**:
- The statement that a planet cannot leave its orbit regardless of the energy supplied is also incorrect. A planet can leave its orbit if it gains enough energy to overcome its binding energy. The binding energy is related to the total mechanical energy, and if sufficient energy is supplied (equal to the negative of the mechanical energy), the planet can escape its orbit.

4. **Conclusion**:
- Based on the analysis:
- The statement about total mechanical energy being negative is **correct**.
- The statement about the orbit being circular is **incorrect**.
- The statement about a planet not being able to leave its orbit is **incorrect**.

### Final Answer:
- The correct statement is: **The total mechanical energy of a planet revolving around the Sun is negative.**