The moon revolves around the earth because the earth exerts a radial force on the moon. Does the earth perform work on the moon?

Options

A. No
B. Yes, sometimes
C. Yes, always
D. Cannot be decided

Answer

To determine whether the Earth performs work on the Moon as it revolves around it, we can analyze the situation step by step.

### Step 1: Understanding the Forces Involved
The Moon revolves around the Earth due to the gravitational force exerted by the Earth on the Moon. This force acts radially inward, towards the center of the Earth.

**Hint:** Identify the type of force acting on the Moon and its direction.

### Step 2: Defining Work Done
Work done (W) is defined as the product of the force (F) applied on an object and the displacement (s) of that object in the direction of the force. Mathematically, it is given by:
\[ W = F \cdot s \cdot \cos(\theta) \]
where \(\theta\) is the angle between the force and the direction of displacement.

**Hint:** Recall the formula for work done and the significance of the angle between force and displacement.

### Step 3: Analyzing the Motion of the Moon
As the Moon revolves around the Earth, its motion is circular. At any point in its orbit, the Moon's velocity is tangential to the circular path, while the gravitational force exerted by the Earth is directed radially inward.

**Hint:** Consider the direction of the Moon's velocity in relation to the gravitational force.

### Step 4: Determining the Angle Between Force and Displacement
Since the gravitational force (radial force) acts towards the center of the Earth and the Moon's displacement (due to its velocity) is tangential to its circular path, the angle \(\theta\) between the force and the displacement is 90 degrees.

**Hint:** Visualize the circular motion and identify the angle between the gravitational force and the Moon's displacement.

### Step 5: Calculating Work Done
Substituting \(\theta = 90^\circ\) into the work done formula, we have:
\[ W = F \cdot s \cdot \cos(90^\circ) \]
Since \(\cos(90^\circ) = 0\), it follows that:
\[ W = F \cdot s \cdot 0 = 0 \]

**Hint:** Remember that the cosine of 90 degrees is zero, leading to zero work done.

### Conclusion
Since the work done by the Earth on the Moon is zero, we conclude that the Earth does not perform work on the Moon as it revolves around it.

**Final Answer:** No, the Earth does not perform work on the Moon.