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A frictionless wedge of mass M = 4m rests on a smooth horizontal floor. A small block of mass m slides toward the wedge with speed v. Friction is absent everywhere (block-wedge and wedge-floor). What is the greatest height the block rises along the wedge surface?

1. 2v²/(5g)
2. v²/g
3. 2v²/(7g)
4. v²/(2g)

Correct answer: 2v²/(5g)

Solution

At peak height both bodies share velocity v_c = mv/(m+M) = v/5; the lost kinetic energy converts to potential energy mgh.

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