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A glass partially filled with water is attached to a wedge that slides without friction down a large inclined plane of angle alpha. The mass of the inclined plane is M and the combined mass of the wedge, glass, and water is m. In the absence of motion the water surface is horizontal. Choose the correct option(s).

1. If the inclined plane is fixed, the free surface of water makes zero angle with the inclined plane in steady state.
2. If the inclined plane is fixed, the angle the water surface makes with the inclined plane depends on m.
3. If the inclined plane is free to move horizontally, the free surface of water makes zero angle with the inclined plane in steady state.
4. If the inclined plane is free to move horizontally, the angle the water surface makes with the inclined plane depends on both m and M.

Correct answer: If the inclined plane is fixed, the free surface of water makes zero angle with the inclined plane in steady state.

Solution

Case 1 (fixed incline): wedge slides with acceleration a = g*sin(alpha) along the slope. Effective gravity in wedge frame = real g minus pseudo-acceleration vector, which points perpendicular to the inclined surface. Water surface is perpendicular to effective g, i.e. parallel to the inclined plane — angle with incline = 0. This is independent of m. So A is correct, B is wrong. Case 2 (free incline): the horizontal acceleration of the incline also plays a role, involving both M and m. The angle is not zero and depends on m and M. So D is correct, C is wrong.

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