Coefficient of restitution for one-dimensional elastic collision is equal to ………

Coefficient of restitution or resilience of two objects can be defined as the constant ratio of relative velocities of after impact to the before impact when the two objects colliding head on together.

Consider two bodies with mass $M$ and $m$.

Before collision ‘$m$’ is at rest, after elastic collision, body $M$ moving with velocity ‘$V$’ collides with ‘$m$’.

As the kinetic energy would be conserved, so $M$ comes to rest and ‘$m$’ moves with velocity ‘$V$’

Coefficient of restitution of two objects is $e=\frac{V-v}{U-u}$

Where, 

$V$ is the separation velocity of body $M$,

$v$ is the velocity of separation of body $m$,

$U$ is the approach velocity of body $M$,

$u$ is the approach velocity of body $m$

After elastic collision, $e=\frac{0-v}{U-0}$

After collision, velocity gets interchanged, then $v=U$

Therefore, $e=1$

The coefficient of restitution for one-dimensional elastic collision is equal to one.

So option 2 is correct.