Question

The first ball of mass m moving witha velocity u collides head on with the second ball of mass m at rest.If the coefficient of restitution is e,then what is the ratio of the velocities of the first and the second ball after the collision?

Answer 1

As no external force is not acting during the collision,we can apply,law of conservation of momentum.

Let,the 1st ball will move with a velocity of `v` and the 2nd one with `x` after the collision.

so, `m u +m*0 = m*v +m*x`

or, `v+x =u` ...1

Now,coefficient of restitution in this case = `(x-v)/(u-0)=e` (coefficient of restitution is defined as the ratio of relative velocity after the collision to relative veocity before the collision)

o, `x-v = eu` .... 2

solving, 1 & 2 we get,

`x= (u(e+1))/2` and , `v= (u(1-e))/2`

So, `v:x = (1-e):(1+e)`