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In the given diagram

enter image description here

assume that all surfaces are frictionless. What is the direction of motion of the centre of mass of the block, the wedge and the whole system?

I am not able to understand why the center of mass of the block moves both horizontally and vertically, while that of the wedge moves only horizontally. But for the entire system the center of mass moves vertically. Please tell me the reason.

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There is no horizontal force on the system (no friction) - but there is a horizontal component of force on the block (due to the direction of the normal force of the wedge). This is why the block can move horizontally.

The only external forces on block and wedge are vertical: gravity (down) and normal force (up). But these do not have to be equal if the center of mass of the system is moving down, which is happening (as the block slides down the wedge the center of mass becomes lower). However the wedge cannot move vertically - this means its center of mass only moves horizontally.

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  • $\begingroup$ The block accelerates downwards. That lowers the center of mass. $\endgroup$ – Floris Dec 2 '17 at 18:18

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