Three balls are identical in size, but differ in their masses. Ball A has a mass

Question

Three balls are identical in size, but differ in their masses. Ball A has a mass m; ball B has a mass 2m, and ball C has a mass 3m. Consider the following cases and determine in which of these linear momentum is conserved. Note that the balls are constrained to move along the x axis and motion in the positive x direction (toward the right) is indicated with a plus sign. Motion in the negative x direction (toward the left) is indicated with a minus sign.

Case I: Ball A is moving at speed +2v to the left of ball B, which is moving at speed –v before an inelastic collision of the two balls occurs. The speed of the two balls after the collision is zero m/s.

Case II: Ball B is moving at speed +2v to the left of ball C, which is moving at speed +v before an inelastic collision of the two balls occurs. The two balls stick together after the collision and have a speed of +2v.

Case III: Ball A is moving at speed +3v to the left of ball C, which is moving at speed +v before an inelastic collision of the two balls occurs. The two balls stick together after the collision and have a speed of +3v/2.

Explanation / Answer

I. 2mv-2mv=3mv' --> v'=0

II. 4mv+3mv=5mv' --> v'=(7/5)v

III. 3mv+3mv=4mv' --> v'=(3/2)v

So, the answer is C.

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