A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision what could be minimum and the maximum value of u.

Explanation

To solve the problem, we need to find the minimum and maximum initial speed \( u \) of a particle of mass 100 g (0.1 kg) that collides with another particle of the same mass initially at rest. After the collision, the total kinetic energy is given as 0.2 J.

### Step-by-Step Solution:

1. **Identify the mass of the particles:**
- Mass of each particle, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \).

2. **Write the expression for initial kinetic energy (KE):**
- The initial kinetic energy of the moving particle is given by:
\[ KE_{\text{initial}} = \frac{1}{2} m u^2 \]
- Substituting the mass:
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.1 \, \text{kg} \times u^2 = 0.05 u^2 \]

3. **Set up the equation for final kinetic energy:**
- The total kinetic energy after the collision is given as 0.2 J:
\[ KE_{\text{final}} = 0.2 \, \text{J} \]

4. **Apply the conservation of kinetic energy:**
- According to the conservation of kinetic energy, we have:
\[ KE_{\text{initial}} = KE_{\text{final}} \]
- Therefore, we can write:
\[ 0.05 u^2 = 0.2 \]

5. **Solve for \( u^2 \):**
- Rearranging the equation gives:
\[ u^2 = \frac{0.2}{0.05} = 4 \]

6. **Calculate the value of \( u \):**
- Taking the square root:
\[ u = \sqrt{4} = 2 \, \text{m/s} \]

7. **Determine the minimum and maximum values of \( u \):**
- Since the collision can be elastic or inelastic, the maximum value of \( u \) occurs in an elastic collision where both particles move after the collision, while the minimum value of \( u \) occurs in a perfectly inelastic collision where they stick together.
- In a perfectly inelastic collision, the final kinetic energy is less than the initial kinetic energy, but since we are given the final kinetic energy, we can conclude that the minimum and maximum value of \( u \) is:
- Minimum \( u = 2 \, \text{m/s} \)
- Maximum \( u = 2 \, \text{m/s} \)

### Final Answer:
- The minimum and maximum value of \( u \) is \( 2 \, \text{m/s} \).