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A ball of mass 'm' moving at a spped 'v' makes a head-on collision with an identical ball at rest . The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

```
11 years ago

```							Hi,

just considr initial vel. of I ball = u

final vel. of I ball = v1
final vel. of II ball =v2

& coeff. of restitution = e

now,
e =  vel. of separaion / vel. of approach

e =  v2 -v1 / u
=> v2-v1 = eu   ....(1)

momentum conservation => mu = mv1 +mv2  => u = v1 + v2          ...(2)

energy eqn  3/4((mu^2)/2)= 1/2*m (v1^2 + v2^2)

=> 3/4*(u^2) = (v1^2 + v2^2)

2*(v1^2 + v2^2)=(v1 + v2)^2  +  (v2 -v1)^2
= u^2  + (eu)^2                   {FROM 1& 2 }
=>         3/2 (u^2) = u^2  + (eu)^2

=>           1/2 (u^2) = (eu)^2

=>              e = root(1/2)

```
11 years ago
```							thanks for the answer
```
9 years ago
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