A body of mass 10 kg moves with a constant speed v of 2 `ms^(-1)` along a circular path of radius 8 m. The power produced by the body will be

Options

A. 10 `Js^(-1)`
B. 98 `Js^(-1)`
C. 49 `Js^(-1)`
D. zero

Explanation

To solve the problem of finding the power produced by a body of mass 10 kg moving with a constant speed of 2 m/s along a circular path of radius 8 m, we can follow these steps:

### Step 1: Understand the motion
The body is moving in a circular path at a constant speed. This means that while the speed is constant, the direction of the velocity is continuously changing.

**Hint:** Remember that in circular motion, the velocity vector is always tangent to the path of the circle.

### Step 2: Identify the forces acting on the body
In circular motion, the body experiences a centripetal force directed towards the center of the circle. This force is necessary to keep the body moving in its circular path.

**Hint:** The centripetal force can be calculated using the formula \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass, \( v \) is the speed, and \( r \) is the radius of the circular path.

### Step 3: Calculate the centripetal force
Using the given values:
- Mass \( m = 10 \, \text{kg} \)
- Speed \( v = 2 \, \text{m/s} \)
- Radius \( r = 8 \, \text{m} \)

The centripetal force \( F_c \) can be calculated as follows:
\[ F_c = \frac{mv^2}{r} = \frac{10 \, \text{kg} \times (2 \, \text{m/s})^2}{8 \, \text{m}} = \frac{10 \times 4}{8} = \frac{40}{8} = 5 \, \text{N} \]

**Hint:** This force is directed towards the center of the circular path.

### Step 4: Determine the power produced
Power is defined as the rate at which work is done. In this case, power \( P \) can be calculated using the formula:
\[ P = \mathbf{F} \cdot \mathbf{v} \]
Where \( \mathbf{F} \) is the force vector and \( \mathbf{v} \) is the velocity vector.

Since the centripetal force is always directed towards the center of the circle and the velocity is tangent to the circle, the angle \( \theta \) between the force and the velocity is 90 degrees.

**Hint:** Recall that \( \cos(90^\circ) = 0 \).

### Step 5: Calculate the power
Substituting the values into the power formula:
\[ P = F \cdot v \cdot \cos(\theta) = 5 \, \text{N} \cdot 2 \, \text{m/s} \cdot \cos(90^\circ) = 5 \cdot 2 \cdot 0 = 0 \, \text{W} \]

### Conclusion
The power produced by the body is \( 0 \, \text{W} \).

**Final Answer:** The correct option is 0 Joules per second.