Question

In an inelastic collision, two bodies with masses $ m_1 = 1\, \text{kg} $ and $ m_2 = 3\, \text{kg} $ collide. Their initial velocities are $ u_1 = 2\, \text{m/s} $ and $ u_2 = 0\, \text{m/s} $, respectively. What is the change in kinetic energy ($ \Delta K $)?

• A. \( 1.0\, \text{J} \)
• B. \( 1.2\, \text{J} \)
• C. \( 1.5\, \text{J} \)
• D. \( 2.0\, \text{J} \)

Hint:

In perfectly inelastic collisions, use conservation of momentum to find final velocity, then compare initial and final kinetic energies to find the loss.

Answer 1

The Correct Option is C

In a perfectly inelastic collision, the final velocity \( v \) of the combined mass is: \[ v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2} = \frac{1 \times 2 + 3 \times 0}{1 + 3} = \frac{2}{4} = 0.5 \, \text{m/s} \] Initial kinetic energy: \[ K_i = \frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} \times 1 \times 2^2 + \frac{1}{2} \times 3 \times 0 = 2 \, \text{J} \] Final kinetic energy: \[ K_f = \frac{1}{2} (m_1 + m_2) v^2 = \frac{1}{2} \times 4 \times (0.5)^2 = \frac{1}{2} \times 4 \times 0.25 = 0.5 \, \text{J} \] Change in kinetic energy: \[ \Delta K = K_i - K_f = 2 - 0.5 = 1.5 \, \text{J} \]