Question

Figure shows a wedge on which a small block is released from rest. All the surfaces are smooth and system comprises of wedge a correct statement(s) regarding motion of block on wedge till block attains maximüm height on wedge.

• A. Acceleration of centre of mass of system is initially vertically down then vertically up.
• B. Initially centre of mass moves down and then up.
• C. At the maximum height block and wedge move with common velocity.
• D. Centre of mass of wedge moves towards left then right

Answer 1

Answer: (C), (D)

At the maximum height block and wedge move with common velocity. Centre of mass of wedge moves towards left then right

Answer 2

The system consists of the block and the wedge. The external forces acting on the system are gravity on the block ($mg$), gravity on the wedge ($Mg$), and the normal force from the ground on the wedge ($N_{ground}$). Since all surfaces are smooth, there is no friction.

• At the maximum height block and wedge move with common velocity: At the maximum height on the wedge, the block's vertical velocity is zero, and its horizontal velocity is equal to the wedge's horizontal velocity. Since the wedge moves only horizontally, they move with a common velocity.

• Centre of mass of wedge moves towards left then right: This is due to horizontal momentum conservation. Initially, the block moves right relative to the wedge, so the wedge moves left. Then the block moves left relative to the wedge, so the wedge moves right.