A string 1 m long can just support a weight of 16 kg. Amass of 1 kg is attached to one of its ends. The body is revolved in a horizontal circle about the other fixed end of the string. Find the greatest number of revolutions made by the mass per second ? (Take g = `10 ms^(-2)`)

Explanation

To solve the problem step by step, we will start by identifying the key elements of the question and applying the relevant physics concepts.

### Step 1: Identify the forces acting on the mass
The mass of 1 kg is attached to a string that can support a maximum weight of 16 kg. The maximum weight can be converted to force using the formula:
\[ F = m \cdot g \]
Where:
- \( m = 16 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)

Calculating the maximum force:
\[ F = 16 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 160 \, \text{N} \]

### Step 2: Relate centripetal force to mass and angular velocity
The centripetal force (\( F_c \)) required to keep the mass moving in a circle is given by:
\[ F_c = m \cdot \omega^2 \cdot r \]
Where:
- \( m = 1 \, \text{kg} \) (mass attached to the string)
- \( r = 1 \, \text{m} \) (length of the string)
- \( \omega \) is the angular velocity in radians per second.

### Step 3: Express angular velocity in terms of revolutions per second
The angular velocity (\( \omega \)) can be expressed in terms of the number of revolutions per second (\( n \)):
\[ \omega = 2\pi n \]

### Step 4: Substitute \( \omega \) into the centripetal force equation
Substituting \( \omega \) into the centripetal force equation gives:
\[ F_c = m \cdot (2\pi n)^2 \cdot r \]
Substituting the known values:
\[ 160 \, \text{N} = 1 \cdot (2\pi n)^2 \cdot 1 \]

### Step 5: Solve for \( n \)
Now, we can simplify and solve for \( n \):
\[ 160 = (2\pi n)^2 \]
\[ 160 = 4\pi^2 n^2 \]
\[ n^2 = \frac{160}{4\pi^2} \]
\[ n^2 = \frac{40}{\pi^2} \]
Taking the square root of both sides:
\[ n = \sqrt{\frac{40}{\pi^2}} \]
\[ n = \frac{\sqrt{40}}{\pi} \]
Using \( \pi \approx 3.14 \):
\[ n \approx \frac{6.32}{3.14} \approx 2.01 \]

### Step 6: Conclusion
The greatest number of revolutions made by the mass per second is approximately:
\[ n \approx 2 \, \text{revolutions per second} \]