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Question

Two balls a and b of same mass are moving on a circular path of radius r=1 m with constant velocity of 5 m/s and 15 m/s as shown in figure. If after some time both ball collides perfectly elastically, find the time t when they will collide again. Friction is absent everywhere.


A
π5 s
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B
2π5 s
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C
π10 s
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D
π s
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Solution

The correct option is A π5 s
As we know after perfectly elastic collision of equal mass object, the velocities get interchanged. Therefore after 1st collision ball a has velocity of 5 m/s and ball b has velocity of 15 m/s


Now, we will find time t when both ball collide again with help of concept of relative motion.
After first collision, velocity of ball b with respect to ball vb,a=vbva=(155) m/s=10 m/s


To collide again after time t, ball b has to travel distance equal to perimeter of circle(2πr) with respect to ball a.
t=2πrvb,a=2×π×110=π5 s

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