A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If $e = c o e f f i c i e n t o f r e s t i t u t i o n$ , then what will be the ratio of velocity of two balls after collision?

\frac{1 - e}{1 + e}

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\frac{e - 1}{e + 1}

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\frac{1 + e}{1 - e}

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\frac{2 + e}{e - 1}

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Solution

The correct option is D $\frac{1 - e}{1 + e}$
Let the initial speed of moving ball be $v$ i.e $u_{1} = v$ and $u_{2} = 0$
The velocities of the balls after collision be $v_{1}$ and $v_{2}$ .
Using $v_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$

$∴$ $v_{1} = \frac{(m - e m) v + 0}{m + m} = \frac{(1 - e) v}{2}$ .........(1)

Using $v_{2} = \frac{(m_{2} - e m_{1}) u_{2} + (1 + e) m_{1} u_{1}}{m_{1} + m_{2}}$

$∴$ $v_{2} = \frac{(m - e m) (0) + (1 + e) m v}{m + m} = \frac{(1 + e) v}{2}$ .........(2)

$⟹$ $\frac{v_{1}}{v_{2}} = \frac{1 - e}{1 + e}$

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A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If e=coefficientofrestitution, then what will be the ratio of velocity of two balls after collision?

A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If $e = c o e f f i c i e n t o f r e s t i t u t i o n$ , then what will be the ratio of velocity of two balls after collision?