Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. B...

Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass \( m \) each and block 2 has mass \( M(Mm) \). Block 2 and block 3 are initially stationary, while block 1 is initially moving towards block 2 with speed \( v \) as shown. Assume that all collisions are head on and perfectly elastic. What value of \( M / m \) ensures that block 1 and block 3 have the same final speed?
(1) \( 5+\sqrt{2} \)
(2) \( 5-\sqrt{2} \)
(3) \( 2+\sqrt{5} \)
(4) \( 3+\sqrt{5} \)