A massless elastic cord (that obeys Hooke's law) break if the tension in the cord exceeds `T_("max")`. One end of the cord is attached to a fixed point, the other is attached to an object of mass 3m as shown in the figure. If a second, smaller object ofmass m moving at an initial speed `v_(0)` strikes the larger mass and the two stick together the cord will stretch and break but the final kinetic energy of the two masses will be zero. If instead the two collide with a perfectly elastic one dimensional collision the cord will still break and the larger mass will move off with a final speed of `v_(f)`. All motion occurs on a horizontal frictionless surface. (Assume that Hooke's law is obeyed throughout untill the cord breaks)

Find `(v_(f))/(v_(0))`

Options

A. `(1)/(sqrt(12))`
B. `(1)/(sqrt(2))`
C. `(1)/(sqrt(6))`
D. `(1)/(sqrt(3))`

Answer

C