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

Explanation

To solve the problem, we need to find the maximum velocity of the stone being whirled in a horizontal circle without breaking the string. We can use the formula for centripetal force, which is provided by the tension in the string.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the stone (m) = 16 kg
- Length of the string (radius of the circle, R) = 144 m
- Maximum tension (T) = 16 N

2. **Use the formula for centripetal force:**
The centripetal force required to keep an object moving in a circle is given by:
\[ T = \frac{m v^2}{R} \]
where:
- T is the tension in the string (which is the maximum force before breaking),
- m is the mass of the stone,
- v is the velocity of the stone,
- R is the radius of the circle.

3. **Substitute the known values into the equation:**
\[ 16 = \frac{16 v^2}{144} \]

4. **Simplify the equation:**
Multiply both sides by 144 to eliminate the denominator:
\[ 16 \times 144 = 16 v^2 \]
This simplifies to:
\[ 2304 = 16 v^2 \]

5. **Divide both sides by 16:**
\[ v^2 = \frac{2304}{16} \]
\[ v^2 = 144 \]

6. **Take the square root of both sides to find v:**
\[ v = \sqrt{144} \]
\[ v = 12 \text{ m/s} \]

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