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]

Create a free account to view solution

View Solution Free
Topic: Momentum and Collision·Practice all Momentum and Collision questions

More Momentum and Collision Questions