A ball moving with a velocity of 12ms^(-1)collideswith another identical stationary ball . After the collision they move as shown in figure . Find the speed of the balls after the collision . Also , decide whether the condition is elastic or not .

A ball moving with a velocity of 12ms^(-1)collideswith another identic

1.	A ball moving with a velocity of 12ms^(-1)collideswith another identical stationary ball . After the collision they move as shown in figure . Find the speed of the balls after the collision . Also , decide whether the condition is elastic or not .
Answer» SOLUTION :Supposethe mass of each ball BEM . Accordingto the law of conservation of momentum bytakingX - components , `mv_(1) =mv_(1) cos 30^(@) +mv_(2)cos 30^(@)` ` :. v_(1) = (sqrt(3))/2 v_(1)+(sqrt(3))/2 v_(2)""....(1)` TakingY - components ` p = mv_(1) sin 30^(@) - mv_(2) sin 30^(@)` ` 0 = (v_(1))/2 - (v_(2))/2 ` ` :. 0 = v_(1)-v_(2)` ` :. ` From equation (1) , Thevelocity before collision`v_(1) =12 m//sand v_(2) = 0 ` ` :. ` The kinetic energy of system before collision `K_(1)=1/2 mv_(1)^(2) +1/2 mv_(2)^(2)` `K_(1) =1/2 xxmxx (12)^(2)` ` K_(1) =72 m J ""....(1)` Velocity after collision `v_(1) =4sqrt(3) m//s and v_(2) = 4sqrt(3) m//s ` ` :. ` The kinetic after of system after collision . `K_(2) =1/2 m xx 48 +1/2 m xx 48` ` :. K_(2) =1/2 m xx 48 +1/2 m xx48` ` :. K_(2) = 24 m + 24 m ` ` :. K_(2) = 48 m J "".....(2)` ` :. ` From equation (1) and (2) , `K_(2) gt K_(2)` so the kinetic energy is not CONSERVED , the collision is not elastic .