A stone tied to the end of a string of length 50 cm is whirled in a horizontal circle with a constant speed . IF the stone makes 40 revolutions in 20 s, then the speed of the stone along the circle is

Options

A. `pi//2 ms^-1`
B. `pi ms^-1`
C. `2pi ms^-1`
D. `4pi ms^-1`

Answer

To solve the problem step by step, we need to find the speed of the stone being whirled in a horizontal circle. Here’s how we can do it:

### Step 1: Identify the radius of the circular motion
The length of the string is given as 50 cm. Since the stone is tied to the end of the string, the radius (r) of the circular motion is equal to the length of the string.

\[ r = 50 \text{ cm} = 0.5 \text{ m} \]

### Step 2: Calculate the angular velocity (ω)
The stone makes 40 revolutions in 20 seconds. To find the angular velocity in radians per second, we first need to convert revolutions to radians.

1 revolution = \(2\pi\) radians, so:

\[ \text{Total radians} = 40 \text{ revolutions} \times 2\pi \text{ radians/revolution} = 80\pi \text{ radians} \]

Now, we divide the total radians by the time in seconds to find the angular velocity:

\[ \omega = \frac{\text{Total radians}}{\text{Time}} = \frac{80\pi \text{ radians}}{20 \text{ s}} = 4\pi \text{ radians/s} \]

### Step 3: Calculate the linear speed (v)
The linear speed (v) of the stone can be calculated using the formula:

\[ v = r \cdot \omega \]

Substituting the values we have:

\[ v = 0.5 \text{ m} \cdot 4\pi \text{ radians/s} = 2\pi \text{ m/s} \]

### Conclusion
The speed of the stone along the circle is:

\[ v = 2\pi \text{ m/s} \]