A light spring is permanently connected between two trolleys of masses $M$ and $m$ which can move over a smooth horizontal table, along a straight line parallel to the length of the spring as shown in figure. The trolleys are brought nearer to compress the spring and then released. In the subsequent motion.

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their center of mass remains stationary.

Angular momentum of system about $O$ is increasing initially.

Initially they move in opposite directions with speeds inversely proportional to their masses.

linear momentum and energy of the system must be conserved.

answer is A, C, D.

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Detailed Solution

No net external force, so linear momentum is conserved, hence $m_{1} \vec{v_{1}} + m_{2} \vec{v_{2}} = 0 i . e v_{1} and v_{2}$ are in opposite direction and $|\frac{v_{1}}{v_{2}}| = \frac{m_{2}}{m_{1}}$ . Spring force is conservative in nature no external force hence number external torque so angular momentum is still conserved.