# Centre of mass problem

I came across a problem where there was an ice and tray system. The system was placed in a gravity free hall. After the ice melted the shift in centre of mass was to be found. But the answer is 0. Is it because Ice won't spread out after melting since there is no gravity? If I m wrong please tell me what's actually happening here. Thanx for any help!

• Are there external forces acting on the ice/water & tray system? – Farcher Apr 17 '19 at 6:42
• COM of this system was initially at rest and will remain at rest because $F_{net}$ on this system by external forces is zero. – user213933 Apr 17 '19 at 7:18
• @Shreyansh Why not write that down as an answer? – Karthik Apr 17 '19 at 8:41
• You're absolutely right, if an ice melts in a gravity free environment, I believe it will remain a ball of water loosing only it well defined shape of an ice. Given no external interaction/force is involved, the center of mass of the system remains the same. – TechDroid Apr 17 '19 at 10:03

Your question has a very standard answer in physics.Whatever I mentioned in my comment I will give a very short note on it here.

See any system of particles has a linear momentum(which may be zero).The linear momentum of the whole system is same as the linear momentum of centre of mass of the system.The linear momentum of a system remains conserved when net external force acting on the system is zero.

In this problem the system is placed in a gravity free space which means that net external force on ice-tray system is always zero. Initially the system has no linear momentum which means the linear momentum of centre of mass of the system is zero. Here the linear momentum remains conserved which means at any point of time whether it is the moment when ice melts or the moment after melting of ice the velocity of centre of mass of the system is zero.

If the centre of mass has not gained velocity it will never shift or change its position.Hope this helps!