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A block of mass m is projected with speed v0 toward a wedge (all surfaces frictionless). The block does not have enough energy to get over the wedge. Which of the following statements is/are correct?

1. When the block reaches its maximum height on the wedge, both block and wedge move with the velocity of the centre of mass of the block-wedge system.
2. The wedge attains its maximum speed relative to the ground when the block returns to the lowest point on the wedge.
3. The momentum of the wedge-block system is conserved at all times.
4. The centre of mass of the wedge-block system remains stationary.

Correct answer: When the block reaches its maximum height on the wedge, both block and wedge move with the velocity of the centre of mass of the block-wedge system.

Solution

At maximum height the block momentarily moves with the wedge at the common centre-of-mass velocity, so option A is correct. Option C is false because total momentum is not conserved (vertical external forces act); the CM is not stationary (it had initial horizontal velocity).

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