A bomb of mass 9 kg explodes into 2 pieces of mass 3 kg and 6 kg. The velocity of mass 3 kg is 1.6 m/s, the K.E. of mass 6 kg is:

Options

A. (a)3.84 J
B. (b)9.6 J
C. (c)1 . 92 J
D. (d)2. 92 J

Explanation

To solve the problem step by step, we will use the principle of conservation of momentum and the formula for kinetic energy.

### Step 1: Understand the system
We have a bomb of mass 9 kg that explodes into two pieces:
- Mass 1 (m1) = 3 kg with a velocity (v1) = 1.6 m/s
- Mass 2 (m2) = 6 kg with an unknown velocity (v2)

### Step 2: Apply the conservation of momentum
Before the explosion, the total momentum of the system is zero since the bomb is at rest. After the explosion, the momentum must still equal zero:
\[ 0 = m1 \cdot v1 + m2 \cdot v2 \]
Substituting the known values:
\[ 0 = (3 \, \text{kg}) \cdot (1.6 \, \text{m/s}) + (6 \, \text{kg}) \cdot v2 \]

### Step 3: Solve for v2
Rearranging the equation to solve for v2:
\[ 6 \, \text{kg} \cdot v2 = - (3 \, \text{kg} \cdot 1.6 \, \text{m/s}) \]
\[ v2 = - \frac{(3 \cdot 1.6)}{6} \]
\[ v2 = - \frac{4.8}{6} \]
\[ v2 = -0.8 \, \text{m/s} \]
(The negative sign indicates that the direction of mass 2 is opposite to that of mass 1.)

### Step 4: Calculate the kinetic energy of mass 2
The formula for kinetic energy (KE) is:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values for mass 2:
\[ KE = \frac{1}{2} \cdot 6 \, \text{kg} \cdot (-0.8 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \cdot 6 \cdot 0.64 \]
\[ KE = 3 \cdot 0.64 \]
\[ KE = 1.92 \, \text{J} \]

### Final Answer
The kinetic energy of mass 6 kg is **1.92 Joules**.

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