When a particle performing uniform circular motion of radius 10 cm undergoes the SHM, what will be its amplitude?

Options

A. 10 cm
B. 5 cm
C. 2.5 cm
D. 20 cm

Explanation

To find the amplitude of a particle performing uniform circular motion that undergoes simple harmonic motion (SHM), we can follow these steps:

### Step 1: Understand the relationship between Uniform Circular Motion and SHM
When a particle moves in uniform circular motion, its projection onto a diameter of the circle will exhibit simple harmonic motion. The key point is that the amplitude of the SHM is equal to the radius of the circular path.

### Step 2: Identify the radius of the circular motion
In this problem, the radius of the circular motion is given as 10 cm.

### Step 3: Relate the radius to the amplitude
Since the amplitude of the SHM is equal to the radius of the circular path, we can conclude that the amplitude of the SHM is also 10 cm.

### Step 4: State the final answer
Thus, the amplitude of the SHM when the particle is performing uniform circular motion with a radius of 10 cm is **10 cm**.

### Summary of the Solution:
- The radius of the circular motion is 10 cm.
- The amplitude of the SHM is equal to the radius.
- Therefore, the amplitude is **10 cm**.