A body of mass 100 g is rotating in a circular path of radius r with constant speed. The work done in one complete revolution is

Options

A. 100 r J
B. `(r)/(100)J`
C. `(100)/(r)J`
D. zero

Answer

To solve the problem of calculating the work done by a body of mass 100 g rotating in a circular path of radius \( r \) with constant speed, we can follow these steps:

### Step 1: Understand the Concept of Work Done
Work done (\( W \)) is defined as the product of the force (\( F \)) applied on an object and the displacement (\( d \)) in the direction of the force. Mathematically, it is given by:
\[ W = F \cdot d = F d \cos \theta \]
where \( \theta \) is the angle between the force and the direction of displacement.

### Step 2: Identify the Forces Acting on the Body
In this case, the body is moving in a circular path, which means it is subject to centripetal force. The centripetal force acts radially inward towards the center of the circular path.

### Step 3: Analyze the Direction of Displacement
As the body rotates, its displacement at any point is tangential to the circular path. Therefore, the direction of displacement is perpendicular to the direction of the centripetal force.

### Step 4: Determine the Angle Between Force and Displacement
Since the centripetal force acts inward (radially) and the displacement is tangential to the circle, the angle \( \theta \) between the centripetal force and the displacement is \( 90^\circ \).

### Step 5: Calculate the Work Done
Using the formula for work done:
\[ W = F d \cos \theta \]
Substituting \( \theta = 90^\circ \):
\[ \cos 90^\circ = 0 \]
Thus, the work done becomes:
\[ W = F d \cdot 0 = 0 \]

### Conclusion
The work done in one complete revolution of the body is:
\[ W = 0 \]

### Final Answer
The work done in one complete revolution is **0 Joules**.

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