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. `F_(1)=2F_(1)`
B. `F_(2)=F_(1)`
C. `F_(2)=3F_(1)`
D. `F_(2)=F//3`

Answer

To solve the problem, we need to understand the relationship between centripetal force, mass, velocity, and radius in circular motion. The centripetal force (Fc) can be expressed using the formula:

\[ F_c = \frac{mv^2}{r} \]

where:
- \( F_c \) 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-by-Step Solution:

1. **Identify the Initial Conditions:**
- Let the initial velocity be \( v \).
- Let the initial radius be \( r \).
- The initial centripetal force \( F_1 \) can be expressed as:
\[ F_1 = \frac{mv^2}{r} \]

2. **Determine the New Conditions:**
- The problem states that both the speed and radius are tripled.
- Therefore, the new velocity \( v' \) will be:
\[ v' = 3v \]
- The new radius \( r' \) will be:
\[ r' = 3r \]

3. **Calculate the New Centripetal Force:**
- We need to find the new centripetal force \( F_2 \) using the new velocity and radius:
\[ F_2 = \frac{m(v')^2}{r'} = \frac{m(3v)^2}{3r} \]
- Simplifying this expression:
\[ F_2 = \frac{m(9v^2)}{3r} = \frac{9mv^2}{3r} = 3 \cdot \frac{mv^2}{r} \]
- Recognizing that \( \frac{mv^2}{r} \) is the original centripetal force \( F_1 \):
\[ F_2 = 3F_1 \]

4. **Conclusion:**
- 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 \( 3F_1 \).