In figure, a hollow tube of mass $\mathrm{M}$ is free in horizontal direction. The system is released from rest. There is no friction present. The tube and blocks are taken as system.

i. Momentum of the system is conserved in $\mathrm{x}$ -direction.
ii. Speed of $\mathrm{A}$ w.r.t. $\mathrm{M}=$ Speed of $\mathrm{B}$ w.r.t. $\mathrm{M}$

¡ii. Trajectory of centre of mass is $\mathrm{X}$ -constant. iv. Centre of mass has finite acceleration.
Evaluate the above statements and choose the correct option from the following:

Two blocks of masses ${\mathrm{m}}_1=2 \mathrm{kg}$ and ${\mathrm{m}}_2=4 \mathrm{kg}$ are moving in the same direction with speeds ${\mathrm{v}}_1=6 \mathrm{m}/\mathrm{s}$ and ${\mathrm{v}}_2=3 \mathrm{m}/\mathrm{s},$ respectively on a frictionless surface as shown in the figure. An ideal spring with spring constant $\mathrm{k}=30000$ $\mathrm{N}/\mathrm{m}$ is attached to the back side of ${\mathrm{m}}_2.$ Then the maximum compression of the spring after collision will be

Block $\mathrm{A}$ is released on the circular track of bigger block $\mathrm{B}$ from rest from the position as shown in figure. Friction is absent everywhere. Choose the correct statement.

A particle of mass $\mathrm{m}=0.2 \mathrm{kg}$ is released from rest from a point $\mathrm{A}$ of a triangular wedge of mass $\mathrm{M}=4.8 \mathrm{kg}$ free to slide on a frictionless horizontal plane. The particle slides down the smooth face $\mathrm{AB}$ of the wedge. When the velocity of the wedge is $0.1 \mathrm{m} {\mathrm{s}}^{-1},$ the velocity of the particle in $\mathrm{m} {\mathrm{s}}^{-1}$ relative to the wedge is

Two persons $A$ and $B$ of weight $80 \mathrm{kg}$ and $50 \mathrm{kg}$ respectively are standing at opposite ends of a boat of mass $70 \mathrm{kg}$ and length $10 \mathrm{m}$ at rest. When they interchange their positions then displacement of the boat will be

Three identical rods of mass $M$ and length $L$ are placed on one another on the table so as to produce the maximum overhang as shown in figure. The maximum total overhang will be