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

VAVB=1−e1+e ,VAVB−1=1−e1+e−1 Or VB−VA=2e1+e.VB But e=VB−VAu Or u=2eVBe(1+e) Or u+eu=2VB u+(VB−VA)=2VB u=VA+VB

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

VAVB=1−e1+e ,VAVB−1=1−e1+e−1 Or VB−VA=2e1+e.VB But e=VB−VAu Or u=2eVBe(1+e) Or u+eu=2VB u+(VB−VA)=2VB u=VA+VB

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A sphere A of mass m moving with a velocity, hits another stationary sphere B of different 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, what is the initial velocity of sphere A with which it strikes?

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$V_{A} + V_{B}$

$V_{A} - V_{B}$

$V_{B} - V_{A}$

$\frac{(V_{A} + V_{B})}{2}$

answer is A.

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Detailed Solution

$\frac{V_{A}}{V_{B}} = \frac{1 - e}{1 + e}$ , $\frac{V_{A}}{V_{B}} - 1 = \frac{1 - e}{1 + e} - 1$

Or $V_{B} - V_{A} = \frac{2 e}{1 + e} . V_{B}$ But $e = \frac{V_{B} - V_{A}}{u}$

Or $u = \frac{2 e V_{B}}{e (1 + e)}$ Or $u + e u = 2 V_{B}$

$\begin{matrix} u + (V_{B} - V_{A}) = 2 V_{B} \\ u = V_{A} + V_{B} \end{matrix}$

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

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