An object A of mass `m` with initial velocity `u` collides with a statinary object B after elestic collision A moves with `(u)/(4)` calculate mass of B.

Options

A. `(7m)/(5)`
B. `(3m)/(5)`
C. `(9m)/(5)`
D. `(4m)/(5)`

Answer

To solve the problem, we will use the principles of conservation of momentum and the fact that the collision is elastic.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Mass of object A, \( m_1 = m \)
- Initial velocity of object A, \( u \)
- Mass of object B, \( m_2 \) (unknown)
- Initial velocity of object B, \( 0 \) (stationary)
- Final velocity of object A after collision, \( v_1 = \frac{u}{4} \)
- Final velocity of object B after collision, \( v_2 \) (unknown)

2. **Use Conservation of Momentum:**
The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
\[ m_1 u + m_2 \cdot 0 = m_1 v_1 + m_2 v_2 \]
Substituting the known values:
\[ m u + 0 = m \left(\frac{u}{4}\right) + m_2 v_2 \]
Simplifying this gives:
\[ mu = \frac{mu}{4} + m_2 v_2 \]

3. **Rearranging the Equation:**
To isolate \( m_2 v_2 \), we can rearrange the equation:
\[ mu - \frac{mu}{4} = m_2 v_2 \]
Factoring out \( mu \):
\[ mu \left(1 - \frac{1}{4}\right) = m_2 v_2 \]
This simplifies to:
\[ mu \left(\frac{3}{4}\right) = m_2 v_2 \]

4. **Express \( v_2 \) in terms of \( u \):**
Since the collision is elastic, we can use the formula for elastic collisions. The relative velocity of approach is equal to the relative velocity of separation:
\[ u - 0 = v_2 - \frac{u}{4} \]
Rearranging gives:
\[ v_2 = u + \frac{u}{4} = \frac{5u}{4} \]

5. **Substituting \( v_2 \) back into the momentum equation:**
Now we substitute \( v_2 \) back into the momentum equation:
\[ mu \left(\frac{3}{4}\right) = m_2 \left(\frac{5u}{4}\right) \]
Canceling \( u \) (assuming \( u \neq 0 \)):
\[ m \left(\frac{3}{4}\right) = m_2 \left(\frac{5}{4}\right) \]

6. **Solving for \( m_2 \):**
Rearranging gives:
\[ m_2 = \frac{3}{5} m \]

### Final Answer:
The mass of object B is \( \frac{3}{5} m \).