Three identical particles A, B and C of mass m lie on a smooth horizontal table. Light inextensible strings which are just taut connect AB and BC and `angleABC` is 135° . An impulse J is imparted to the particle C in the direction BC. Mass of each particle is m. Choose the correct options.

Options

A. Speed of A just after the impulse imparted is `(sqrt(2)J)/(7m)`
B. Speed of B just after the impulse imparted is `(sqrt(10)J)/(7m)`
C. Speed of C just after the impulse imparted is `(3J)/(7m)`
D. Speed of A just after the impulse imparted is `(2J)/(7m)`

Explanation

`(J_(2))/(sqrt(2))=2mv_(1) (J_(2))/(sqrt(2))=mv_(2)rArr v_(2)=2v_(1)`
`J-J_(2)=m/(sqrt(2))(v_(1)+v_(2))`
`J-2sqrt(2)mv_(1)=(3mv_(1))/(sqrt(2))rArr J=(7mv_(1))/(sqrt(2))rArr v_(1)=(sqrt(2)J)/(7m)`
`v_(2)=(2sqrt(2)J)/(7m)`
`v_(A)=v_(1)=(sqrt(2)J)/(7m), v_(B)=(sqrt(10)J)/(7m)`
`v_(c)=(v_(1)+v_(2))/(sqrt(2))=(3J)/(7m)`