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Block A (mass m) rests on top of Block B (mass m) placed on a frictionless surface. There is friction between A and B. At t = 0, block A moves to the right at 6 m/s and block B moves to the right at 3 m/s. Which of the following statements is/are correct?

1. a_com = 0
2. v_com = 4.5 m/s
3. v_AB = 3 m/s at t = 0
4. Velocity of A when slipping stops = 4.5 m/s

Correct answer: v_com = 4.5 m/s

Solution

Since there is no external horizontal force (floor is frictionless), the center of mass velocity remains constant throughout. v_com = (6+3)/2 = 4.5 m/s. When slipping stops, both A and B move at 4.5 m/s. Also a_com = 0 since no external horizontal force. The relative velocity v_AB = 6 - 3 = 3 m/s at t=0.

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