Question

A ball of mass m moving at a speed v based on head on collision with identical balls at rest the kinetic energy

Answer 1

Mass of first ball = m

Speed of first ball = v

Mass of second ball = m

Let final velocities of first and second ball are v₁ and v₂ respectively.

Using law of conservation of momentum,

m(v₁ + v₂) = mv

v₁ + v₂ = v Equation 1

And , v₁ - v₂ = ev Equation 2

Given:-

Final Kinetic Energy = 3/4 Initial Kinetic Energy

(1/2)mv₁² + (1/2)mv₂² = (3/4) x 1/2 mv²

v₁² + v₂² = (3/4) v²

[(v₁ + v₂)² + (v₁ - v₂)² ] / 2 = 3v² / 4

(1 + e²)v² / 2 = 3v² / 4

1 + e² = 3/2

e² = 1/2

e = 1 / √2

Hope it helps!