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 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:
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In inelastic collisions, kinetic energy is not conserved, and you must calculate the initial and final energies to find the fraction lost.
Updated On: Jun 6, 2025
- \(\frac{1}{2}\)
- \(\frac{2}{3}\)
- \(\frac{3}{4}\)
- \(\frac{1}{3}\)
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The Correct Option is A
Solution and Explanation
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:
\[
\frac{1}{2}.
\]
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