A wheel of diameter 20 cm is rotating 600 rpm. The linear velocity of particle at its rim is

Options

A. `6.28 cm//s`
B. `62 .8 cm //s`
C. `0.628 cm//s`
D. `628.4 cm //s`

Explanation

To find the linear velocity of a particle at the rim of a wheel with a given diameter and rotational speed, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the radius of the wheel:**
The diameter of the wheel is given as 20 cm. The radius (r) can be calculated as:
\[ r = \frac{\text{diameter}}{2} = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm} \]

2. **Convert the rotational speed from rpm to rps:**
The wheel rotates at 600 revolutions per minute (rpm). To convert this to revolutions per second (rps), we divide by 60:
\[ N = \frac{600 \, \text{rpm}}{60} = 10 \, \text{rps} \]

3. **Calculate the angular velocity (ω):**
The angular velocity in radians per second can be calculated using the formula:
\[ \omega = 2 \pi N \]
Substituting the value of N:
\[ \omega = 2 \pi \times 10 = 20 \pi \, \text{radians/second} \]

4. **Calculate the linear velocity (V):**
The linear velocity (V) of a point on the rim of the wheel is given by the formula:
\[ V = r \omega \]
Substituting the values of r and ω:
\[ V = 10 \, \text{cm} \times 20 \pi \, \text{radians/second} = 200 \pi \, \text{cm/second} \]

5. **Calculate the numerical value of the linear velocity:**
Using the approximate value of π (3.14):
\[ V \approx 200 \times 3.14 = 628 \, \text{cm/second} \]

### Final Answer:
The linear velocity of the particle at the rim of the wheel is approximately **628 cm/second**.

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