A smooth small spherical ball of mass m, moving with velocity u collides head on with another small

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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

Accepted Answer

Sol.$e = \frac{V_{2} - V_{1}}{u}$ ...(i)mu = mv1 + 3mv2 ...(ii)$\frac{1}{3} 	imes \left( \frac{1}{2}mu^{2} ight) = \frac{1}{2}mv_{1}^{2} + \frac{1}{2}3mv_{2}^{2}$ ...(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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