Momentum and CollisionHardBloom L3
Question
A smooth small spherical ball of mass m, moving with velocity u collides head on with another small spherical ball of mass m, which was initially at rest. One - third of the initial kinetic energy of the system is lost. The coefficient of restitution between the spheres is
Options
A.$\frac{1}{3}$
B.$\frac{1}{\sqrt{3}}$
C.$\frac{1}{2}$
D.zero
Solution
Sol.
$e = \frac{V_{2} - V_{1}}{u}$ ...(i)
mu = mv1 + 3mv2 ...(ii)
$\frac{1}{3} \times \left( \frac{1}{2}mu^{2} \right) = \frac{1}{2}mv_{1}^{2} + \frac{1}{2}3mv_{2}^{2}$ ...(iii)
Solving, $v_{1} = \frac{(1 - 3e)}{4}u$, $v_{2} = \frac{(1 + e)}{4}u$
Alternate : ∆KE = $\frac{1}{2}\mu v_{rel}^{2}(1 - e^{2})$ [ μ = reduced mass, vrel = initial relative velocity]
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