A ball of mass m , moving with a speed 2v_(0) collides inelastically ( e gt 0) with an identicalball at rest . Show that (a) For head - on collision , both the balls move forward . (b) For a general collision , the angle between the two velocities of scattered balls is less than 90^(@)

A ball of mass m , moving with a speed 2v_(0) collides inelastically (

1.	A ball of mass m , moving with a speed 2v_(0) collides inelastically ( e gt 0) with an identicalball at rest . Show that (a) For head - on collision , both the balls move forward . (b) For a general collision , the angle between the two velocities of scattered balls is less than 90^(@)
Answer» Solution :(a) Let `v_(1) and v_(2)` are velocities of the two balls after collision . From law of CONSERVATION of linear momentum , `2mv_(0)=mv_(1)+mv_(2)` ` :. 2v_(0) =v_(1)+v_(2)` and `e= (v_(2)-v_(1))/(2v_(0)) rArr v_(2)=v_(1) +2v_(0)e` ` :. 2v_(1)=2v_(0)-2ev_(0)` ` :. v_(1)=v_(0)(1-e)` Since , `e lt 1 rArr v_(1)` has the same sign as `v_(0)` therefore , the ball moves on after collision . (b) Consider the diagram below for general collision . From the law of conservation of linear momentum , `P=P_(1)+P_(2)` For inelastic collision some KE is lost , hence `(p^(2))/(2m)gt(p_(1)^(2))/(2m)+(p_(2)^(2))/(2m)` `p^(2)gt p_(1)^(2)+p_(2)^(2)` THUS , p,`p_(1) and p_(2)` are related as shown in the FIGURE. `theta` is acute (less than `90^(@)`) `(p^(2)=p_(1)^(2)+p_(2)^(2) "WOULD be given if " theta =90^(@))`