In Fig. there are n identical suspended with wires of equal length. The spheres are almost in contact with each other. Sphere 1 is pulled aside and released. If sphere 1 strikes sphere 2 with velocity u. find an expression for velocity v_(n) of the nth sphere immediately after being struck by the one adjacent to it. The coefficient of restitution for all the impacts is e.

In Fig. there are n identical suspended with wires of equal length. Th

1.	In Fig. there are n identical suspended with wires of equal length. The spheres are almost in contact with each other. Sphere 1 is pulled aside and released. If sphere 1 strikes sphere 2 with velocity u. find an expression for velocity v_(n) of the nth sphere immediately after being struck by the one adjacent to it. The coefficient of restitution for all the impacts is e.
Answer» Solution :LET velocities of SPHERE `1` and `2` after COLLISION be `v_(1)` and `v_(2)`, respectively, then `(v_(2)-v_(1))/u=e` and `mv_(2)+mv_(1)="mu"` From above equations `v_(2)=((1+e)u)/2` Now sphere `2` will collide with sphere `3` and affter collision velocity of `3` can be formed as `v_(3)=((1+e)/2)^(2)u` Hence, similarly velocity of `nth` sphere can be formed as `v_(N)=((1+e)/2)^(n-1)u`