A point size body is moving along a circle at an angular velocity `2.8rads^(-1)`. If centripetal acceleration of body is `7ms^(-2)` then its speed is

Options

A. `1.25 ms^(-1)`
B. `2.5 ms^(-1)`
C. `3.5 ms^(-1)`
D. `7ms^(-1)`

Answer

To solve the problem, we need to find the speed of a point-sized body moving in a circle given its angular velocity and centripetal acceleration.

### Step-by-Step Solution:

1. **Identify the given values:**
- Angular velocity (\( \omega \)) = \( 2.8 \, \text{radians/second} \)
- Centripetal acceleration (\( a_c \)) = \( 7 \, \text{m/s}^2 \)

2. **Use the formula for centripetal acceleration:**
The formula for centripetal acceleration is given by:
\[ a_c = \frac{v^2}{r} \]
where \( v \) is the linear speed and \( r \) is the radius of the circular path.

3. **Express \( r \) in terms of \( v \) and \( \omega \):**
The relationship between linear speed \( v \), angular velocity \( \omega \), and radius \( r \) is:
\[ v = \omega \cdot r \]
Rearranging gives:
\[ r = \frac{v}{\omega} \]

4. **Substitute \( r \) into the centripetal acceleration formula:**
Substitute \( r \) from step 3 into the centripetal acceleration formula:
\[ a_c = \frac{v^2}{\frac{v}{\omega}} = \frac{v^2 \cdot \omega}{v} = v \cdot \omega \]
Therefore, we can express \( v \) in terms of \( a_c \) and \( \omega \):
\[ v = \frac{a_c}{\omega} \]

5. **Plug in the values:**
Now substitute the known values of \( a_c \) and \( \omega \):
\[ v = \frac{7 \, \text{m/s}^2}{2.8 \, \text{radians/second}} = 2.5 \, \text{m/s} \]

6. **Final answer:**
The speed of the body is:
\[ v = 2.5 \, \text{m/s} \]

### Summary:
The speed of the point-sized body moving in a circle with an angular velocity of \( 2.8 \, \text{radians/second} \) and a centripetal acceleration of \( 7 \, \text{m/s}^2 \) is \( 2.5 \, \text{m/s} \).