A body of mass 10 kg moving with speed of `3 ms ^(-1)` collides with another stationary body of mass 5 kg As a result, the two bodies stick togethre. The KE of composite mass will be

Options

A. 30 J
B. 60 J
C. 90 J
D. 120 J

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We have a body of mass \( m_1 = 10 \, \text{kg} \) moving with a speed \( v_1 = 3 \, \text{m/s} \) and another stationary body of mass \( m_2 = 5 \, \text{kg} \). After the collision, the two bodies stick together.

### Step 2: Apply the Law of Conservation of Momentum
The total momentum before the collision must equal the total momentum after the collision.

**Before Collision:**
- Momentum of the first body: \( p_1 = m_1 \cdot v_1 = 10 \, \text{kg} \cdot 3 \, \text{m/s} = 30 \, \text{kg m/s} \)
- Momentum of the second body (stationary): \( p_2 = m_2 \cdot 0 = 0 \, \text{kg m/s} \)

**Total Momentum Before Collision:**
\[ p_{\text{total before}} = p_1 + p_2 = 30 + 0 = 30 \, \text{kg m/s} \]

**After Collision:**
Let \( V \) be the common velocity of the two bodies after the collision. The total mass after the collision is \( m_1 + m_2 = 10 + 5 = 15 \, \text{kg} \).

**Total Momentum After Collision:**
\[ p_{\text{total after}} = (m_1 + m_2) \cdot V = 15 \cdot V \]

Setting the total momentum before and after equal gives us:
\[ 30 = 15V \]

### Step 3: Solve for V
To find \( V \):
\[ V = \frac{30}{15} = 2 \, \text{m/s} \]

### Step 4: Calculate the Kinetic Energy of the Composite Mass
The kinetic energy (KE) of the composite mass after the collision can be calculated using the formula:
\[ KE = \frac{1}{2} (m_1 + m_2) V^2 \]

Substituting the values:
\[ KE = \frac{1}{2} \cdot 15 \cdot (2)^2 \]
\[ KE = \frac{1}{2} \cdot 15 \cdot 4 \]
\[ KE = \frac{1}{2} \cdot 60 = 30 \, \text{Joules} \]

### Final Answer
The kinetic energy of the composite mass after the collision is **30 Joules**.

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