A bob of mass 10 kg is attached to wire 0.3 m long. Its breaking stress is `4.8 xx 10^(7) N//m^(2)`. The area of cross section of the wire is `10^(-6) m^(2)`. The maximum angular velocity with which it can be rotated in a horizontal circle

Explanation

To find the maximum angular velocity with which the bob can be rotated in a horizontal circle, we can follow these steps:

### Step 1: Understand the relationship between stress, force, and area
The breaking stress (σ) of the wire is given by the formula:
\[ \sigma = \frac{F}{A} \]
where:
- \( F \) is the force acting on the wire,
- \( A \) is the area of cross-section of the wire.

### Step 2: Calculate the maximum force the wire can withstand
Rearranging the formula for stress, we can express the maximum force (F_max) as:
\[ F_{\text{max}} = \sigma_{\text{max}} \times A \]
Substituting the given values:
- \( \sigma_{\text{max}} = 4.8 \times 10^7 \, \text{N/m}^2 \)
- \( A = 10^{-6} \, \text{m}^2 \)

Calculating \( F_{\text{max}} \):
\[ F_{\text{max}} = 4.8 \times 10^7 \times 10^{-6} = 48 \, \text{N} \]

### Step 3: Relate the force to angular velocity
The force acting on the bob when it is rotating in a circle is given by:
\[ F = m \cdot r \cdot \omega^2 \]
where:
- \( m \) is the mass of the bob,
- \( r \) is the radius of the circle (which is equal to the length of the wire),
- \( \omega \) is the angular velocity.

### Step 4: Substitute the known values
Here, the mass \( m = 10 \, \text{kg} \) and the radius \( r = 0.3 \, \text{m} \). We can substitute these into the force equation:
\[ F_{\text{max}} = m \cdot r \cdot \omega^2 \]
Substituting the known values:
\[ 48 = 10 \cdot 0.3 \cdot \omega^2 \]

### Step 5: Solve for angular velocity
Rearranging the equation to solve for \( \omega^2 \):
\[ \omega^2 = \frac{48}{10 \cdot 0.3} = \frac{48}{3} = 16 \]
Taking the square root to find \( \omega \):
\[ \omega = \sqrt{16} = 4 \, \text{radians/second} \]

### Conclusion
The maximum angular velocity with which the bob can be rotated in a horizontal circle is:
\[ \omega_{\text{max}} = 4 \, \text{radians/second} \]

---