A positively charged particle of mass m moves towards another positive point charge of equal mass initially at rest in free space. At the point of closest approach, the total kinetic energy is 1/n times the first particle’s initial kinetic energy. Find n.
Physics · Mixed Chapter
JEE Mains

Question

A positively charged particle of mass m moves towards another positive point charge of equal mass initially at rest in free space. At the point of closest approach, the total kinetic energy is 1/n times the first particle’s initial kinetic energy. Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Initial momentum and kinetic energy: One charged particle of mass m moves at speed u towards an identical stationary particle. The initial momentum is mu, and initial kinetic energy is ½mu². Step 2 — Condition at closest approach: At the minimum separation, their relative radial speed becomes zero. Both equal masses momentarily have the same speed v. Step 3 — Momentum conservation: mu = 2mv ⇒ v = u/2. Step 4 — Kinetic-energy ratio: Total kinetic energy then = 2×½m(u/2)² = mu²/4, which…