Two identical balls A and B. each of mass 2 kg and radius R, are suspended vertically from inextensible strings as shown in Fig. The third ball C of mass 1 kg and radius r=(sqrt(2)-1)R falls and hits A and B symmetrically with 10 m//s. Speed of both A and B just after the collision is 3 m//s. speed of C just asfter collision is

Two identical balls A and B. each of mass 2 kg and radius R, are suspe

1.	Two identical balls A and B. each of mass 2 kg and radius R, are suspended vertically from inextensible strings as shown in Fig. The third ball C of mass 1 kg and radius r=(sqrt(2)-1)R falls and hits A and B symmetrically with 10 m//s. Speed of both A and B just after the collision is 3 m//s. speed of C just asfter collision is
Answer» `2m//s` `2sqrt(2)m//s` `5m//s` `(sqrt(2)-1)m//s` SOLUTION :First calculate `theta=45^(@)`. As the balls `A` and `B` are constained to move HORIZONTALLY (immediately after collision) if `'I'` be the IMPULSE impated by ball `C` to each of `A` and `B`, the mpulse received by ball `C` from them would be `2Isintheta` Now, each of ball `B` and `C` received impulse `'I'` as shown in figure. but moves impulse IMPARTED to ball `B` and `C` by the respective strings and hence, `Icostheta=M_(A)V_(A)=M_(B)V_(B)` Now, for ball `C` if its final velocity is `V_(C)^(')` downwards we have `M_(C)V_(C)^(')=M_(C)V_(C)-2Isintheta` `impliesV_(C)^(')=V_(C)-2(MA)/(MC)V_(A)` (`:'theta=45^(@))` `=-2m//s` (`-ve` sign indcates that it is directed upwards)