A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton . The maximum velocity of revolution that can be given to the stone without breaking it, will be

Options

A. `20 ms^(-1)`
B. `16 ms^(-1)`
C. `14 ms^(-1)`
D. `12 ms^(-1)`

Answer

To find the maximum velocity of the stone being whirled in a horizontal circle without breaking the string, we can use the relationship between tension, mass, velocity, and radius in circular motion.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the stone (m) = 16 kg
- Length of the string (radius, r) = 144 m
- Maximum tension (T) = 16 N

2. **Understand the Formula for Tension in Circular Motion:**
The tension in the string provides the centripetal force required to keep the stone moving in a circle. The formula for tension (T) in terms of mass (m), velocity (v), and radius (r) is:
\[ T = \frac{m v^2}{r} \]

3. **Rearranging the Formula:**
To find the maximum velocity (v), we can rearrange the formula:
\[ v^2 = \frac{T \cdot r}{m} \]
\[ v = \sqrt{\frac{T \cdot r}{m}} \]

4. **Substituting the Values:**
Now, substitute the known values into the equation:
\[ v = \sqrt{\frac{16 \, \text{N} \cdot 144 \, \text{m}}{16 \, \text{kg}}} \]

5. **Calculating the Velocity:**
Simplifying the expression:
\[ v = \sqrt{\frac{2304 \, \text{N m}}{16 \, \text{kg}}} \]
\[ v = \sqrt{144 \, \text{m}^2/\text{s}^2} \]
\[ v = 12 \, \text{m/s} \]

6. **Conclusion:**
The maximum velocity of revolution that can be given to the stone without breaking the string is **12 m/s**.