If the frequency of an object in unifrom circular motion is doubled, its acceleration becomes

Options

A. Two times
B. Four times
C. Half
D. one fourth

Answer

To solve the problem, we need to understand the relationship between frequency and acceleration in uniform circular motion.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
In uniform circular motion, the centripetal acceleration \( a \) is given by the formula:
\[ a = 4 \pi^2 r f^2 \]
where \( r \) is the radius of the circular path and \( f \) is the frequency of the motion.

2. **Doubling the Frequency**:
If the frequency \( f \) is doubled, we can express the new frequency as:
\[ f' = 2f \]

3. **Calculating the New Acceleration**:
We substitute \( f' \) into the acceleration formula:
\[ a' = 4 \pi^2 r (f')^2 = 4 \pi^2 r (2f)^2 \]
Simplifying this gives:
\[ a' = 4 \pi^2 r (4f^2) = 16 \pi^2 r f^2 \]

4. **Comparing New Acceleration to Original Acceleration**:
The original acceleration \( a \) can be expressed as:
\[ a = 4 \pi^2 r f^2 \]
Now, we can relate the new acceleration \( a' \) to the original acceleration \( a \):
\[ a' = 4 \times a \]

5. **Conclusion**:
Therefore, if the frequency of the object in uniform circular motion is doubled, the acceleration becomes \( 4 \) times the original acceleration.

### Final Answer:
The acceleration becomes **4 times**.

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