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The 'e' Equation

Two balls A...

Question

Two balls $A$ and $B$ having masses $1 k g$ and $2 k g$ moving with speeds $21 m / s$ and $4 m / s$ respectively in opposite direction, collide head on. After collision $A$ moves with a speed of $1 m / s$ in the same direction, then the coefficient of restitution is :

0.1

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0.2

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0.4

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None

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Solution

The correct option is D $0.2$
Mass of ball A $m_{A} = 1 k g$ and its velocity before collision $u_{A} = 21 m / s$
Mass of ball B $m_{B} = 2 k g$ and its velocity before collision $u_{B} = - 4 m / s$ (since it is moving in opposite direction)
Velocity of ball A after collision $v_{A} = 1 m / s$
Using $v_{A} = \frac{(m_{A} - e m_{B}) u_{A} + (1 + e) m_{B} u_{B}}{m_{A} + m_{B}}$
Or $1 = \frac{(1 - 2 e) (21) + (1 + e) (2) (- 4)}{1 + 2}$
Or $1 = \frac{13 - 50 e}{3}$
$⟹ e = 0.2$

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Two balls A and B having masses 1kg and 2kg moving with speeds 21m/s and 4m/s respectively in opposite direction, collide head on. After collision A moves with a speed of 1m/s in the same direction, then the coefficient of restitution is :

Two balls $A$ and $B$ having masses $1 k g$ and $2 k g$ moving with speeds $21 m / s$ and $4 m / s$ respectively in opposite direction, collide head on. After collision $A$ moves with a speed of $1 m / s$ in the same direction, then the coefficient of restitution is :