Question

A sphere of mass m moving with constant velocity u hits another stationary sphere of the same mass. If e is the coefficient of restitution, the ratio of velocities ($v₁/v₂$) after collision will be:

• A. $\frac1-e1+e$
• B. $\frac1+e1-e$
• C. $\frace+11-e$
• D. $\frace-1e+1$

Hint:

For equal masses, $v₁ = \frac1-e2u$, $v₂ = \frac1+e2u$.

Answer 1

The Correct Option is A

Step 1: Conservation of momentum: $mu = mv₁ + mv₂ → u = v₁ + v₂$.

Step 2: $e = \fracv₂ - v₁u$. Solving: $v₁ = \frac1-e2u$, $v₂ = \frac1+e2u$. Ratio = $\frac1-e1+e$.