Question

a sphere of m mass moving with a constant velocity hits another stationary sphere of the same mass. if e is the coefficient of restitution, then ratio of speed of first sphere to the speed of the second sphere after collision wiil be​

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, mu+m⋅0=m⋅v+m⋅x

or, v+x=u ...1

Now,coefficient of restitution in this case = x−vu−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)