Question

A ball of mass m collides head on with another ball at rest. The KE of the system left is 50%. Find the coefficient of restitution.

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{\sqrt{2}}{3}$
• C. $\frac{1}{2}$
• D. Zero

Answer 1

Answer: (D)

Zero

Answer 2

mu + 0 = mv₁ + mv₂

or u = v₁ + v₂ …………. (i)

e = $\frac{v_{2} - v_{1}}{u}$ or eu = v₂ – v₁ …….. (ii)

From (i) and (ii) v₁ = $\frac{(1 - e)u}{2}$ and

v₁ = $\frac{(1 - e)u}{2}\left\lbrack \frac{1}{2}mv^{2} \right\rbrack \times \frac{1}{2}$

= $\frac{1}{2}m\left\lbrack \left( \frac{(1 - e)u}{2} \right)^{2} + \left( \frac{(1 + e)u}{2} \right)^{2} \right\rbrack 1$

= 1 + e² or e = 0