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Question: Which of the following is true when an object of mass m moving on a horizontal frictionless surface hits and sticks to an object of mass M > m, which is initially at rest on the surface?
The system will move with a velocity less than the initial velocity of the smaller mass object, but in the same direction. This is due to the principle of conservation of momentum. Before the collision, the momentum is "m*v" (assuming v is the initial velocity of the smaller object) and after the collision the momentum becomes "(m+M)*u" where "u" is the velocity of combined mass. Therefore, setting these two equal (since momentum is conserved), we have m*v = (m+M)*u. It can be concluded that "u" or the final velocity is less than the initial velocity "v" when M > m.
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