Consider a gravity free hall in which a tray of mas M, carrying a cubical block of icce of mas m and edge L, is at rest in the middle.. If the ice melts, by what distnce does the centre of mass of the tray plus the ice system descend?

Explanation

Initially centre of mass of block of ice is at a height a/2 from the surface of vessel and finally when ice melta then due to large diameter of vessel height of the water formed is negligibly small. So centre of mass of water can be assumed at the surface of vessel, hence we can understand that in the process of melting centre of mass of ice comes down by a distance 4y - a/2. There is no change in the vessel hence its centre of mass remains at the same place. So we can say that displacement of centre of mass of vessel is zero, Ay,=0. Displacement of centre of mass can be written as follows:
`Deltay=(m_(1)Deltay_(1)+m_(2)Deltay_(2))/(m_(1)+m_(2))`
`rArr Delta y=(mxx(a)/(2)+Mxx0)/(m+M)=(ma)/(2(m+M))`