A body of moment of inertia of `3 kg m^(2)` rotating with an angular velocity of 2 rad/s has the same kinetic energy as that that of mass 12 kg moving with a velocity of

Options

A. 1 m/s
B. 2 m/s
C. 4 m/s
D. 8 m/s

Explanation

To solve the problem, we need to find the velocity of a mass of 12 kg that has the same kinetic energy as a rotating body with a moment of inertia of 3 kg m² and an angular velocity of 2 rad/s.

### Step-by-Step Solution:

1. **Identify the given values:**
- Moment of inertia (I) = 3 kg m²
- Angular velocity (ω) = 2 rad/s
- Mass (m) = 12 kg

2. **Write the formula for rotational kinetic energy (KE_rot):**
\[ KE_{\text{rot}} = \frac{1}{2} I \omega^2 \]

3. **Substitute the values into the rotational kinetic energy formula:**
\[ KE_{\text{rot}} = \frac{1}{2} \times 3 \, \text{kg m}^2 \times (2 \, \text{rad/s})^2 \]

4. **Calculate ω²:**
\[ (2 \, \text{rad/s})^2 = 4 \, \text{rad}^2/\text{s}^2 \]

5. **Calculate the rotational kinetic energy:**
\[ KE_{\text{rot}} = \frac{1}{2} \times 3 \times 4 = \frac{12}{2} = 6 \, \text{J} \]

6. **Write the formula for translational kinetic energy (KE_trans):**
\[ KE_{\text{trans}} = \frac{1}{2} m v^2 \]

7. **Set the two kinetic energies equal to each other:**
\[ KE_{\text{rot}} = KE_{\text{trans}} \implies 6 = \frac{1}{2} \times 12 \times v^2 \]

8. **Simplify the equation:**
\[ 6 = 6 v^2 \]

9. **Divide both sides by 6:**
\[ 1 = v^2 \]

10. **Take the square root of both sides:**
\[ v = \pm 1 \, \text{m/s} \]

11. **Since speed cannot be negative, we take the positive value:**
\[ v = 1 \, \text{m/s} \]

### Final Answer:
The velocity of the mass moving with the same kinetic energy is **1 m/s**.