A sphere of mass m moving with velocity v collides head-on with...

A sphere of mass

m

moving with velocity

v

collides head-on with another sphere of the same mass at rest. If the coefficient of restitution

e = \dfrac{1}{2}

, then what is the ratio of final velocity of the second sphere to the initial velocity of the first sphere? A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If the

A sphere of mass m moving with velocity v collides head-on with another sphere of the same mass at rest. If the

Correct answer

0.75

Step-by-step solution

mv + 0 = {mv}_{1} + {mv}_{2}

{v}_{1} + {v}_{2} = v

....(i)

e = \dfrac{{v}_{2} - {v}_{1}}{v - 0}

ev = {v}_{2} - {v}_{1}

..(ii)

Add equation (i) & equation (ii)

ev + v = 2{v}_{2}

{v}_{2} = \dfrac{v( e + 1 )}{2}

\dfrac{{v}_{2}}{v} = \dfrac{e + 1}{2} = 0 . 75

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