A particle moves along a circle of radius 10 cm . If its linear speed changes from 4m/s to 5 m/s in 1 s, then its angular acceleration will be

Options

A. 2 rad /`s^(2)`
B. 5 rad /`s^(2)`
C. 10 rad /`s^(2)`
D. 8 rad /`s^(2)`

Explanation

To find the angular acceleration of a particle moving along a circular path, we can follow these steps:

### Step 1: Identify the given values
- Initial linear speed (V_initial) = 4 m/s
- Final linear speed (V_final) = 5 m/s
- Time interval (Δt) = 1 s
- Radius of the circle (r) = 10 cm = 0.1 m (conversion from cm to m)

### Step 2: Calculate the change in linear speed (ΔV)
\[ \Delta V = V_{final} - V_{initial} = 5 \, \text{m/s} - 4 \, \text{m/s} = 1 \, \text{m/s} \]

### Step 3: Calculate the tangential acceleration (a_t)
Tangential acceleration (a_t) is given by the formula:
\[ a_t = \frac{\Delta V}{\Delta t} \]
Substituting the values:
\[ a_t = \frac{1 \, \text{m/s}}{1 \, \text{s}} = 1 \, \text{m/s}^2 \]

### Step 4: Calculate the angular acceleration (α)
Angular acceleration (α) is related to tangential acceleration by the formula:
\[ \alpha = \frac{a_t}{r} \]
Substituting the values (remembering to convert radius to meters):
\[ \alpha = \frac{1 \, \text{m/s}^2}{0.1 \, \text{m}} = 10 \, \text{radians/s}^2 \]

### Final Answer
The angular acceleration (α) is:
\[ \alpha = 10 \, \text{radians/s}^2 \]

---