If a body of 5 kg is moving in a circle of radius 5 m with a velocity 100 m `s^(-1)`, then the centripetal force acting on the body is

Options

A. 100 N
B. `10^4 N`
C. `10^3 N`
D. `10N`

Explanation

To find the centripetal force acting on a body moving in a circle, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body (m) = 5 kg
- Radius of the circle (r) = 5 m
- Velocity of the body (v) = 100 m/s

### Step 2: Use the formula for centripetal acceleration
The formula for centripetal acceleration (a_c) is given by:
\[ a_c = \frac{v^2}{r} \]

### Step 3: Substitute the values into the formula for centripetal acceleration
Substituting the values we have:
\[ a_c = \frac{(100 \, \text{m/s})^2}{5 \, \text{m}} = \frac{10000 \, \text{m}^2/\text{s}^2}{5 \, \text{m}} = 2000 \, \text{m/s}^2 \]

### Step 4: Calculate the centripetal force
The centripetal force (F_c) can be calculated using the formula:
\[ F_c = m \cdot a_c \]
Substituting the mass and the centripetal acceleration:
\[ F_c = 5 \, \text{kg} \cdot 2000 \, \text{m/s}^2 = 10000 \, \text{N} \]

### Final Answer
The centripetal force acting on the body is **10000 N**.

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