Question

A body of mass \(m\) moving along a straight line collides with a stationary body of mass \(2m\). After collision if the two bodies move together with the same velocity, then the fraction of kinetic energy lost in the process is:

• A. \(\frac{1}{2}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{3}{4}\)
• D. \(\frac{1}{3}\)

Hint:

In inelastic collisions, kinetic energy is not conserved, and you must calculate the initial and final energies to find the fraction lost.

Answer 1

The Correct Option is A

In an inelastic collision, the total kinetic energy is not conserved. To find the fraction of kinetic energy lost, we use the equation: \[ \text{Fraction of energy lost} = \frac{KE_{\text{initial}} - KE_{\text{final}}}{KE_{\text{initial}}}. \] Given that the bodies move together after collision, the final velocity can be found using the conservation of momentum: \[ (m . v_1) = (3m . v_f), \] where \(v_1\) is the initial velocity of the first body and \(v_f\) is the final velocity after collision. After calculating, we find that the fraction of energy lost is: \[ \frac{1}{2}. \]