A body of mass `1kg` is moving with a uniform speed of `1m//s` in a circular path of radius `1m`. The external force acting on the body is

Options

A. `1N`
B. 1 dyne
C. `1J`
D. zero

Explanation

To find the external force acting on a body moving in a circular path, we can use the concept of centripetal force. Here’s a step-by-step solution:

### Step 1: Identify the parameters
- Mass of the body (m) = 1 kg
- Speed of the body (v) = 1 m/s
- Radius of the circular path (r) = 1 m

### Step 2: Understand the concept of centripetal force
When an object moves in a circular path at a constant speed, it experiences a centripetal force directed towards the center of the circular path. This force is necessary to keep the object moving in that circular path.

### Step 3: Use the formula for centripetal force
The formula for centripetal force (F_c) is given by:
\[ F_c = \frac{mv^2}{r} \]
where:
- \( m \) = mass of the body
- \( v \) = speed of the body
- \( r \) = radius of the circular path

### Step 4: Substitute the values into the formula
Now, substituting the values into the formula:
\[ F_c = \frac{(1 \, \text{kg}) \cdot (1 \, \text{m/s})^2}{1 \, \text{m}} \]

### Step 5: Calculate the centripetal force
Calculating the above expression:
\[ F_c = \frac{1 \cdot 1}{1} = 1 \, \text{N} \]

### Conclusion
The external force acting on the body is a centripetal force of 1 Newton directed towards the center of the circular path.

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