Solving the Centre of Mass Shift When Ice Melts

[ritwik06]

SOLVED

Homework Statement

A plate of of Mass m contains an ice cube of mass M and side L. Find the shift in centre of mass when th ice melts.
(Gravity absent)

The Attempt at a Solution

I think that the centre of mass will come down by ML/2(M+m)
But my book gives it zero. why?
What has gravity to do with centre of mass?? And yes, what's the difference between centre of gravity an centre of mass?

 

[LowlyPion]

Homework Statement

A plate of of Mass m contains an ice cube of mass M and side L. Find the shift in centre of mass when th ice melts.
(Gravity absent)

The Attempt at a Solution

I think that the centre of mass will come down by ML/2(M+m)
But my book gives it zero. why?
What has gravity to do with centre of mass?? And yes, what's the difference between centre of gravity an centre of mass?

The point of no gravity is that the masses M and m will not move relative to each other. Hence there will be no change.

If there is gravity, then it will cause the water to collapse to the plate and the center of mass would lower by some function of M,m,L.

The center of gravity is the point about which an object will balance. But it's center of mass may be anywhere along the vertical above the center of gravity.

 

[ritwik06]

The point of no gravity is that the masses M and m will not move relative to each other. Hence there will be no change.

If there is gravity, then it will cause the water to collapse to the plate and the center of mass would lower by some function of M,m,L.

The center of gravity is the point about which an object will balance. But it's center of mass may be anywhere along the vertical above the center of gravity.

Thanks a lot.