Three blocks $\mathrm { A } , \mathrm { B }$ and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, $m$ while C has mass $M$. Block A is given an initial speed $v$ towards B due to which it collides with B perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically . $\frac { 5 } { 6 }$ th of the initial kinetic energy is lost in the whole process. What is the value of $M / m$ ?
(1) 3
(2) 4
(3) 5
(4) 2

Three objects $A , B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A , B$ and $C$ are $m , 2 m$ and $2 m$ respectively. $A$ moves towards $B$ with a speed of $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is:
(1) $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$