Identify the incorrect statement about a planet revolving around Sun

Options

A. The gravitational attraction provides the centripetal force for a revolving planet
B. The total energy of a planet is always negative
C. The total energy of a planet is always more than potential energy of the system
D. Kinetic energy of revolving planet is sometimes zero

Answer

To identify the incorrect statement about a planet revolving around the Sun, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** The gravitational attraction provides the centripetal force for a revolving planet.

**Explanation:**
The gravitational force acting between the planet and the Sun indeed acts as the centripetal force that keeps the planet in its orbit. The gravitational force \( F_g \) can be expressed as:

\[ F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where \( G \) is the gravitational constant, \( m_1 \) is the mass of the Sun, \( m_2 \) is the mass of the planet, and \( r \) is the distance between the centers of the two bodies.

This gravitational force is equal to the centripetal force required to keep the planet in circular motion:

\[ F_c = \frac{m \cdot v^2}{r} \]

Since \( F_g = F_c \), this statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement:** The total energy of a planet is always negative.

**Explanation:**
The total energy \( E \) of a planet in orbit is the sum of its kinetic energy \( K \) and potential energy \( U \):

\[ E = K + U \]

The kinetic energy \( K \) is given by:

\[ K = \frac{G \cdot m_1 \cdot m_2}{2r} \]

The potential energy \( U \) is given by:

\[ U = -\frac{G \cdot m_1 \cdot m_2}{r} \]

Thus, the total energy can be calculated as:

\[ E = \frac{G \cdot m_1 \cdot m_2}{2r} - \frac{G \cdot m_1 \cdot m_2}{r} = -\frac{G \cdot m_1 \cdot m_2}{2r} \]

Since this value is negative, this statement is **correct**.

### Step 3: Analyze the Third Statement
**Statement:** The total energy of a planet is always more than the potential energy of the system.

**Explanation:**
From our previous calculation, we found that:

\[ E = -\frac{G \cdot m_1 \cdot m_2}{2r} \]
\[ U = -\frac{G \cdot m_1 \cdot m_2}{r} \]

Since \( E \) is negative and less than \( U \) (which is also negative but has a larger magnitude), we can conclude that the total energy \( E \) is actually less than the potential energy \( U \). Therefore, this statement is **incorrect**.

### Step 4: Analyze the Fourth Statement
**Statement:** Kinetic energy of the revolving planet is sometimes zero.

**Explanation:**
The kinetic energy \( K \) of the planet is given by:

\[ K = \frac{G \cdot m_1 \cdot m_2}{2r} \]

Since both \( G \), \( m_1 \), \( m_2 \), and \( r \) are always positive values, the kinetic energy cannot be zero. Thus, this statement is **correct**.

### Conclusion:
The incorrect statement is: **The total energy of a planet is always more than the potential energy of the system.**