The torque on a planet about the centre of sun is

Options

A. Zero
B. Negative
C. Positive
D. Depend on mass of planet

Answer

To find the torque on a planet about the center of the Sun, we can follow these steps:

### Step 1: Understand the Concept of Torque
Torque (\( \tau \)) is defined as the rotational equivalent of linear force. It is calculated using the formula:
\[ \tau = \mathbf{r} \times \mathbf{F} \]
where \( \mathbf{r} \) is the position vector from the pivot point (in this case, the center of the Sun) to the point of application of the force, and \( \mathbf{F} \) is the force acting on the object (the planet).

### Step 2: Identify the Forces Acting on the Planet
In this scenario, the gravitational force (\( \mathbf{F} \)) acting on the planet is directed towards the center of the Sun. The position vector (\( \mathbf{r} \)) points from the center of the Sun to the planet.

### Step 3: Determine the Angle Between the Vectors
Since the force of gravity acts towards the Sun and the position vector points away from the Sun, the angle (\( \theta \)) between the position vector (\( \mathbf{r} \)) and the force vector (\( \mathbf{F} \)) is \( 180^\circ \).

### Step 4: Calculate the Torque
Using the torque formula:
\[ \tau = rF \sin(\theta) \]
Substituting \( \theta = 180^\circ \):
\[ \tau = rF \sin(180^\circ) \]
Since \( \sin(180^\circ) = 0 \):
\[ \tau = rF \cdot 0 = 0 \]

### Step 5: Conclusion
The torque on the planet about the center of the Sun is \( 0 \). This means that the gravitational force does not create any rotational effect on the planet about the Sun.

### Final Answer
The torque on a planet about the center of the Sun is **0**.

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