In the figure `S_(1)` and `S_(2)` are two light springs of stiffness k and 4k respectively. When springs are in relaxed state, seperation between their free ends is `2x_(0)` . A uniform solid cylinder of mass m and radius R`( lt x_(0))` is placed exactly midway between the free ends of the springs with its axis horizontal and perpendicular to the springs . Now consider the two cases separately.

Case I : The cylinder is imparted speed `v_(0)` towards left. When the cylinder comes to rest momentarily the co-ordinates of its centre are either (`-x_(1), R)` or `(x_(2),R)` .
Case II: The Cylinder is imparted speed `v_(0)` toward left and angular speed `omega^(0)` in clockwise sense simultaneously . At the time of maximum compression in the springs the co-ordinates of centre of the cylinder are either `(-x_(3),R) " or "(x_(4),R)` Now answer the following questions assuming that friction is absent every where.
Choose the correct option

Options

A. `x_(1)=x_(2)`
B. `x_(1)=x_(3)`
C. `x_(1)=x_(4)`
D. `x_(3)=x_(4)`

Answer

B