Two small particles of equal masses stant moving in opposite direction from a point `A` in a burtizonetal circule orbic their tangention velocity are `V` and `2V` , respectively as shown in the figure between collsions , the particals move with constant speed After making how many elastic collition , other the then that at `A` these two partical will again reach the point `A` ?

Options

A. `4`
B. `3`
C. `2`
D. `1`

Answer

C

Explanation

(c ) Let the radius of the circle be `r` . Then the two distance travelled by the two particles befor first colision is `2 pi r` .Therefor
`2 pi xx 1 xx v xx1 = 2 pi r `
where t is the time taken for first collision to cocur
` t = (2 pi r)/(3v)`

:. Distance travelled by particle with velocity `v` is equal to `v= xx (2 pi r)/(3v) = ( (2 pi r)/(3)`
Therefor the collcion at `B`
,
As the collsion is elastic and the particle have equal masses , the velocity will interchange as shown in the figure . According to the same reasoning as above , the `2nd` collsion will take place at `C` and the velocity will again interchange
With the same reasoning the `3^(nd) ` collsion will accur at the point `A` . This there will be two elestic collasion befor the parcle again reach at `A` .