A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8 kg mass is 6 m/sec. The kinetic energy of the other mass is

Options

A. 48 J
B. 32 J
C. 24 J
D. 288 J

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We have a bomb with a total mass of 12 kg that explodes into two pieces: one piece has a mass of 4 kg and the other has a mass of 8 kg. The velocity of the 8 kg piece is given as 6 m/s. We need to find the kinetic energy of the 4 kg piece.

### Step 2: Apply the law of conservation of momentum
Since the bomb was initially at rest, the total initial momentum is zero. According to the conservation of momentum, the total momentum after the explosion must also be zero.

Let \( v \) be the velocity of the 4 kg piece. The momentum of the 8 kg piece is given by:
\[ \text{Momentum of 8 kg piece} = 8 \, \text{kg} \times 6 \, \text{m/s} = 48 \, \text{kg m/s} \]

For the 4 kg piece, its momentum will be:
\[ \text{Momentum of 4 kg piece} = 4 \, \text{kg} \times v \]

Setting the total momentum to zero:
\[ 4v - 48 = 0 \]

### Step 3: Solve for \( v \)
Rearranging the equation gives:
\[ 4v = 48 \]
\[ v = \frac{48}{4} = 12 \, \text{m/s} \]

### Step 4: Calculate the kinetic energy of the 4 kg piece
The kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values for the 4 kg piece:
\[ KE = \frac{1}{2} \times 4 \, \text{kg} \times (12 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 4 \times 144 \]
\[ KE = 2 \times 144 = 288 \, \text{J} \]

### Final Answer
The kinetic energy of the other mass (4 kg) is **288 Joules**.

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