Question

A bomb of mass \(20\,kg\) at rest explodes into two pieces of masses \(12\,kg\) and \(8\,kg\). If the velocity of \(8\,kg\) mass is \(6\,ms^{-1}\), then the kinetic energy of the other mass is:

• A. \(144\,J\)
• B. \(64\,J\)
• C. \(86\,J\)
• D. \(96\,J\)

Hint:

In explosion problems, always use conservation of momentum first, then calculate energy.

Answer 1

The Correct Option is D

Step 1: Apply conservation of momentum.
Initially, bomb is at rest, so total momentum is zero.
\[ p_{\text{initial}} = 0 \]

Step 2: Momentum after explosion.
\[ m_1 v_1 + m_2 v_2 = 0 \]

Step 3: Substitute values.
\[ 12v_1 + 8 \times 6 = 0 \]
\[ 12v_1 + 48 = 0 \]

Step 4: Solve for velocity of \(12\,kg\) mass.
\[ v_1 = -4\,ms^{-1} \]

Step 5: Calculate kinetic energy.
\[ K = \frac{1}{2}mv^2 \]
\[ K = \frac{1}{2} \times 12 \times (4)^2 \]

Step 6: Compute value.
\[ K = 6 \times 16 = 96\,J \]

Step 7: Final conclusion.
\[ \boxed{96\,J} \] Hence, correct answer is option (D).