1. Tardigrade
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  4. A sphere of mass m moving with constant velocity μ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

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Q. A sphere of mass m moving with constant velocity $ \mu $ , collides with another stationary sphere of same mass. If e is the coefficient of restitution, the ratio of the final velocities of the first and second spheres is

EAMCETEAMCET 2007

Solution:

Let $ {{v}_{1}},{{v}_{2}} $ be the final velocities of the two spheres. Applying the law of conservation of linear momentum $ mu=m({{v}_{1}}+{{v}_{2}}) $ or $ {{v}_{1}}+{{v}_{2}}=u $ ?(i) Again the coefficient of restitution is given by $ e=\frac{{{v}_{2}}-{{v}_{1}}}{u} $ or $ {{v}_{2}}-{{v}_{1}}=eu $ ?(ii) Solving Eqs. (i) and (ii), we get $ {{v}_{1}}=\frac{u}{2}(1-e),{{v}_{2}}=\frac{u}{2}(1+e) $ Therefore, $ \frac{{{v}_{1}}}{{{v}_{2}}}=\left( \frac{1-e}{1+e} \right) $