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

Options

A. `2 ms^(-1)`
B. `16 ms^(-1)`
C. `14 ms^(-1)`
D. `12 ms^(-1)`

Explanation

To find the maximum velocity of a stone of mass 16 kg attached to a string of length 144 m that is whirled in a horizontal circle, we can follow these steps:

### Step 1: Understand the Forces Involved
In circular motion, the tension in the string provides the centripetal force required to keep the stone moving in a circle. The formula for centripetal force is given by:

\[ F_c = \frac{mv^2}{r} \]

where:
- \( F_c \) is the centripetal force,
- \( m \) is the mass of the stone,
- \( v \) is the velocity,
- \( r \) is the radius of the circular path.

### Step 2: Set Up the Equation
Since the maximum tension the string can withstand is given as 16 N, we can set the maximum tension equal to the centripetal force:

\[ T_{\text{max}} = \frac{mv^2}{r} \]

Substituting the known values:
- \( T_{\text{max}} = 16 \, \text{N} \)
- \( m = 16 \, \text{kg} \)
- \( r = 144 \, \text{m} \)

We can rewrite the equation as:

\[ 16 = \frac{16v^2}{144} \]

### Step 3: Solve for Velocity
To find \( v^2 \), we can rearrange the equation:

\[ 16 \times 144 = 16v^2 \]

Dividing both sides by 16:

\[ 144 = v^2 \]

Now, taking the square root of both sides gives:

\[ v = \sqrt{144} = 12 \, \text{m/s} \]

### Step 4: Conclusion
The maximum velocity of the stone that can be given without breaking the string is:

\[ \boxed{12 \, \text{m/s}} \]

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