A 4m mass travelling at speed u elastically collides head-on with a stationary 2m mass. What fraction of the first body's initial kinetic energy is lost?
Options

Question

A 4m mass travelling at speed u elastically collides head-on with a stationary 2m mass. What fraction of the first body's initial kinetic energy is lost?

G1 Physics · Accepted Answer

Step 1 — Principle: For a one-dimensional elastic collision, conserve momentum and kinetic energy. Step 2 — Working: In elastic 1D collision, the 4m mass has final speed v=[(4m-2m)/(4m+2m)]u=u/3. Step 3 — Working: Its retained KE fraction=(v/u)²=1/9, so lost fraction=1-1/9=8/9. Correct answer: A — 8/9.