First slide

Collisions

Question

A sphere A of mass m moving with certain velocity hits another stationery sphere B of different mass. If the ratio of velocities of the spheres after collision is $\frac{V_{A}}{V_{B}} = \frac{1 - e}{1 + e}$ , where ‘e’ is coefficient of restitution. The initial velocity of sphere A with which it strikes is,

Moderate

A

$V_{A} + V_{B}$
B

$V_{A} - V_{B}$
C

$V_{B} - V_{A}$
D

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

Solution

$g i v e n \frac{V_{A}}{V_{B}} = \frac{1 - e}{1 + e} cross multiply$
$\Rightarrow e = \frac{V_{B} - V_{A}}{V_{A} + V_{B}} ---(1)$
$by definition , e = \frac{V_{2} - V_{1}}{u_{1} - u_{2}} = \frac{V_{B} - V_{A}}{u_{A} - 0} ---(2) s u b s t i t u t e e q n (1) i n (2) \Rightarrow u_{A} = V_{A} + V_{B}$

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