If the speed and radius both are trippled for a body moving on a circular path, then the new centripetal force will be:

Options

A. (a)`F_(1)=2F_(1)`
B. (b)`F_(2)=F_(1)`
C. (c)`F_(2)=3F_(1)`
D. (d)`F_(2)=F//3`

Answer

To solve the problem, we need to determine how the centripetal force changes when both the speed and the radius of a body moving in a circular path are tripled.

### Step-by-Step Solution:

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

2. **Identify the initial centripetal force**:
Let the initial centripetal force be \( F_1 \):
\[ F_1 = \frac{mv^2}{r} \]

3. **Determine the new speed and radius**:
If both the speed and the radius are tripled, we have:
- New speed \( v_1 = 3v \)
- New radius \( r_1 = 3r \)

4. **Calculate the new centripetal force**:
The new centripetal force \( F_2 \) can be expressed as:
\[ F_2 = \frac{m(v_1)^2}{r_1} \]
Substituting the new values:
\[ F_2 = \frac{m(3v)^2}{3r} \]
Simplifying this:
\[ F_2 = \frac{m \cdot 9v^2}{3r} = \frac{9mv^2}{3r} = 3 \cdot \frac{mv^2}{r} \]

5. **Relate the new force to the initial force**:
From the previous step, we see that:
\[ F_2 = 3F_1 \]

6. **Conclusion**:
Therefore, the new centripetal force \( F_2 \) is three times the initial centripetal force \( F_1 \):
\[ F_2 = 3F_1 \]

### Final Answer:
The new centripetal force will be \( 3 \) times the initial centripetal force.