A bomb of mass `30 kg` at rest explodes into two pieces of mass `18 kg` and `12 kg`. The velocity of mass `18 kg is 6 m//s`. The kinetic energy of the other mass is

Options

A. 256J
B. 486J
C. 524J
D. 324J

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the conservation of momentum
The initial momentum of the system (the bomb) is zero since it is at rest. After the explosion, the momentum of the two pieces must also sum to zero.

### Step 2: Set up the momentum equation
Let the velocity of the 12 kg mass be \( V \). The momentum before the explosion is:
\[ \text{Initial momentum} = 0 \]
The momentum after the explosion is:
\[ \text{Final momentum} = (18 \, \text{kg} \times 6 \, \text{m/s}) + (12 \, \text{kg} \times V) \]
Setting the initial momentum equal to the final momentum gives us:
\[ 0 = (18 \times 6) + (12 \times V) \]

### Step 3: Solve for \( V \)
Rearranging the equation:
\[ 12V = - (18 \times 6) \]
\[ V = - \frac{18 \times 6}{12} \]
Calculating \( V \):
\[ V = -9 \, \text{m/s} \]

### Step 4: Calculate the kinetic energy of the 12 kg mass
The formula for kinetic energy (\( KE \)) is given by:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values for the 12 kg mass:
\[ KE = \frac{1}{2} \times 12 \times (-9)^2 \]
Calculating:
\[ KE = \frac{1}{2} \times 12 \times 81 \]
\[ KE = 6 \times 81 = 486 \, \text{Joules} \]

### Final Answer
The kinetic energy of the 12 kg mass is **486 Joules**.

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