In a collinear collision a particle with an intial speed v_(0) strike a stationary particle of the same mass. If the final total kinetic energy is 50 % greater than theoriginal kinetic energythe magnitude of the relative velocitybetween the twoparticles after collision is .

In a collinear collision a particle with an intial speed v_(0) strike

1.	In a collinear collision a particle with an intial speed v_(0) strike a stationary particle of the same mass. If the final total kinetic energy is 50 % greater than theoriginal kinetic energythe magnitude of the relative velocitybetween the twoparticles after collision is .
Answer» `(v_(0))/4` `sqrt(2) v_(0)` `(v_(0))/2` `(v_(0))/(sqrt(2))` Solution :Initial Kinetic energy = `1/2 mv_(0)^(2)` FINAL Kinetic energy = 50 % of `1/2 mv_(0)^(2) +1/2 mv_(0)^(2)` ` = 1/2 mv_(0)^(2)+1/2 mv_(0)^(2) xx1/2 ` `= 3/4mv_(0)^(2)` . `:. 1/2 mv_(1)^(2) +1/2 mv_(2)^(2) = 3/4 mv_(0)^(2)` ` :. v_(1)^(2) +v_(2)^(2)=v_(0)` ` :. v_(1)^(2) +2v_(1)v_(2) +v_(2)^(2) =v_(0)^(2) ""....(2)` ` rArr` From ewu . (1) and (2) `2v_(1)v_(2) =v_(0)^(2) -3/2v_(0)^(2) [ :. v_(1)^(2) +v_(2)^(2) =3/2v_(0)^(2)]` ` :. 2v_(1)v_(2) = - (v_(0)^(2))/2 ` and `(v_(1)-v_(2))^(2) = v_(1)^(2)+v_(2)^(2) -2v_(1)V_(2)` `= 3/2 v_(0)^(2) - (-(v_(0)^(2))/2)` ` =3/2 v_(0)^(2) +(v_(0)^(2))/2` ` = 2v_(0)^(2)` ` :. v_(1) - v_(2) = sqrt(2) v_(0)` Relative velocity .