If the centripetal force acting on a body revolving along a circular path of radius 25 m is 200 N, its KE is

Options

A. A) 2.5 KJ
B. B) 4 KJ
C. C) 4.8 KJ
D. D) 6 J

Answer

To solve the problem, we need to find the kinetic energy (KE) of a body that is revolving in a circular path with a given centripetal force and radius. Here are the steps to find the solution:

### Step 1: Understand the relationship between centripetal force, mass, and velocity.
The centripetal force (F) acting on a body moving in a circular path is given by the formula:
\[ F = \frac{m v^2}{r} \]
where:
- \( F \) is the centripetal force,
- \( m \) is the mass of the body,
- \( v \) is the velocity of the body,
- \( r \) is the radius of the circular path.

### Step 2: Substitute the known values into the formula.
From the problem, we have:
- \( F = 200 \, \text{N} \)
- \( r = 25 \, \text{m} \)

Substituting these values into the centripetal force formula:
\[ 200 = \frac{m v^2}{25} \]

### Step 3: Rearrange the equation to find \( m v^2 \).
Multiplying both sides by 25 gives:
\[ m v^2 = 200 \times 25 \]
\[ m v^2 = 5000 \, \text{kg m}^2/\text{s}^2 \]

### Step 4: Use the kinetic energy formula.
The kinetic energy (KE) of the body is given by:
\[ KE = \frac{1}{2} m v^2 \]

### Step 5: Substitute \( m v^2 \) into the kinetic energy formula.
Now substituting \( m v^2 = 5000 \):
\[ KE = \frac{1}{2} \times 5000 \]
\[ KE = 2500 \, \text{J} \]

### Step 6: Convert Joules to kilojoules.
Since \( 1 \, \text{kJ} = 1000 \, \text{J} \):
\[ KE = 2.5 \, \text{kJ} \]

### Final Answer:
The kinetic energy of the body is \( 2.5 \, \text{kJ} \).

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