Two blocks `A` and `B` of masses in and `2m` respectively placed on a smooth floor are connected by a spring. A third body `C` of mass `m` moves with velocity `v_(0)` along the line joining `A` and `B` and collides elastically with `A`. At a certain instant of time after collision it is found that the instantaneous velocities of `A` and `B` are same then:
A. the common velocity of `A` and `B` at time `t_(0)` is `v//3`
B. the spring constant is `k=(mv_(0)^(2))/(2x_(0)^(2))`
C. the spring constant is `k=(2mv_(0)^(2))/(3x_(0)^(2))`
D. none of these