A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass- if the ratio of the velocities of the spheres after collision is vA-vB-1-e-1-e where e is the coefficient of restitution- waht is the initial velocity of spheres A with which it strikes-

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The 'e' Equation

A sphere A of...

Question

A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. if the ratio of the velocities of the spheres after collision is $\frac{v_{A}}{v_{B}} = \frac{1 - e}{1 + e}$ where e is the coefficient of restitution, waht is the initial velocity of spheres A with which it strikes?

\frac{v_{A}}{v_{B}}

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- \frac{v_{A}}{v_{B}}

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\frac{v_{B}}{- v_{A}}

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(\frac{v_{A} + v_{B}}{2})

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Solution

The correct option is A $\frac{v_{A}}{v_{B}}$
Let $v_{A}$ & $v_{B}$ be the velocity after collision in the same diameter by momentum correction
$m v_{A} + m v_{B} = m v$
$1 v_{A} + v_{B} = v$
Explain newton law
restitution along common normal
$\frac{v_{B} - v_{A}}{0 - v_{A}} = - e$ $\frac{r e l a t i v e v e l o c i t y o f s e p a r a t i o n}{r e l a t i o n v e l o c i t y o f a p p r o a c h} = - e$
$v_{B} - v_{A} = e v$
$- v_{A} + v_{B} = e v$
$2 v_{B} = (1 + e) v \Rightarrow v_{B} (\frac{1 + e}{2}) v$
$v_{A} = (\frac{1 - e}{2}) v$
$∴ \frac{v_{A}}{v_{B}} = (\frac{1 - e}{1 + e})$

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A sphere A of mass m moving with a velocity hits another stationary sphere B of same mass. if the ratio of the velocities of the spheres after collision is vAvB=1−e1+e where e is the coefficient of restitution, waht is the initial velocity of spheres A with which it strikes?