Elastic Collision Energy Conservation

Steps:

• Compute initial kinetic energy: each sphere has $\frac{1}{2}mv^2$, so total KE before = $mv^2$.
• For head-on elastic collision of equal masses, velocities reverse directions post-impact, maintaining speeds at $v$.
• Thus, total KE after = $mv^2$, same as before.
• Verify momentum: initial total p = $mv + (-mv) = 0$, conserved as final p = 0.

Why B is correct:

• In elastic collisions, total kinetic energy is conserved, so post-impact KE equals pre-impact KE of $mv^2$.

Why the others are wrong:

• A: Elastic collisions do not cause sticking; that's inelastic.
• C: Pre-impact KE is $mv^2$, not $2mv^2$.
• D: Pre-impact momentum is zero (opposing directions), not $2mv$.

Final answer: B